<DOCUMENT>
<TYPE>N-CSRS
<SEQUENCE>1
<FILENAME>b0404ncsr.txt
<TEXT>
<PAGE>
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-CSR

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                         MANAGEMENT INVESTMENT COMPANIES

                  Investment Company Act file number: 811-2151
                  --------------------------------------------

                         BANCROFT CONVERTIBLE FUND, INC.

-------------------------------------------------------------------------------
               (Exact name of registrant as specified in charter)

               65 Madison Avenue, Morristown, New Jersey 07960-7308
-------------------------------------------------------------------------------
               (Address of principal executive offices) (Zip code)

                               Thomas H. Dinsmore
                        Bancroft Convertible Fund, Inc.
                               65 Madison Avenue
                       Morristown, New Jersey 07960-7308
                     (Name and address of agent for service)

                                    Copy to:
                              Martha J. Hays, Esq.
                      Ballard Spahr Andrews & Ingersoll, LLP
                               1735 Market Street
                          Philadelphia, PA 19103-7599


        Registrant's telephone number, including area code: 973-631-1177

Date of fiscal year end:  October 31

Date of reporting period:  April 30, 2004

<Page>
ITEM 1. REPORTS TO STOCKHOLDERS.

Include a copy of the report transmitted to stockholders pursuant to Rule 30e-1
under the Act (17 CFR 270.30e-1).

<PAGE>

                           BANCROFT CONVERTIBLE FUND



                            2004 Semi-Annual Report
                                 April 30, 2004
<PAGE>

                             2004 Semi-Annual Report
                                 April 30, 2004

Bancroft Convertible Fund, Inc. (the "Fund") operates as a closed-end,
diversified management investment company and invests primarily in convertible
securities, with the objectives of providing income and the potential for
capital appreciation -- which objectives the Fund considers to be relatively
equal, over the long-term, due to the nature of the securities in which it
invests.

                                   Highlights

Performance through April 30, 2004 with dividends reinvested

<TABLE>
<CAPTION>
                                                        4 Months      1 Year     5 Years      10 Years
                                                        --------     --------    -------      --------
<S>                                                      <C>           <C>        <C>         <C>
Bancroft market value (a) ............................   (1.01)%       0.41%      32.10%      174.87%
Bancroft net asset value (b) .........................    0.08         9.98       17.79       147.81
Closed-end convertible fund average (b) ..............    1.21        17.18       23.46       122.10
S&P 500 (a) ..........................................    0.10        22.88      (10.78)      193.25
Russell 2000 (a) .....................................    0.85        42.05       38.64       154.61(b)
Lehman Aggregate Bond Total Return Index (b) .........   (0.01)        1.82       38.03       103.13
</TABLE>

Performance data represent past results and do not reflect future performance.

(a) From Bloomberg L.P. pricing service.
(b) From Lipper, Inc. Closed-End Fund Performance Analysis, dated
    April 30, 2004.

--------------------------------------------------------------------------------

Quarterly History of NAV and Market Price

<TABLE>
<CAPTION>
                         Net Asset Values             Market Prices (AMEX, symbol BCV)
Qtr. Ended     High          Low        Close        High          Low         Close
----------    ------        ------      ------       ------       ------       ------
<S>           <C>           <C>         <C>          <C>          <C>          <C>
Jul. 03       $20.58        $19.55      $20.02       $19.85       $18.95       $19.80
Oct. 03        20.84         19.61       20.84        19.70        19.05        19.70
Jan. 04        21.75         20.73       21.51        20.14        18.59        19.59
Apr. 04        21.79         20.79       20.79        19.74        18.35        18.35
</TABLE>

--------------------------------------------------------------------------------

Dividend Distributions (12 Months)

<TABLE>
<CAPTION>
Record            Payment                              Capital
Date              Date              Income              Gains          Total
------            --------          ------             -------        -------
<S>               <C>               <C>                 <C>           <C>
 6/13/03           6/27/03          $0.160              $ --          $0.160
 9/18/03           9/29/03           0.160                --           0.160
11/28/03          12/26/03           0.210                --           0.210
 3/16/04           3/30/04           0.170                --           0.170
                                    ------              ------        ------
                                    $0.700                --          $0.700
                                    ======              ======        ======
</TABLE>

BANCROFT CONVERTIBLE FUND

To Our Shareholders

The economic expansion continues to develop as non-farm payrolls have increased
by over one million in 2004.  As usually occurs in such expansions, interest
rates have gone up.  Over the past six months interest rates have gone from
approximately 3% to 4% on five year U.S. Treasury bonds, from 4.3% to 5% on five
year BBB (investment  grade) bonds and from 6.9% to 7.5% on five year B
industrial bonds.  Other maturities have seen similar rises in rates.  So, even
though the Federal Reserve Board has not raised rates yet, the bond market has.

Oil prices appear to have topped out for now, but we expect they may remain in a
range of $35-$40 per barrel rather than the old expectation of $22-$28 per
barrel.  Further, gasoline prices should remain high as the refineries that make
gasoline for our cars and trucks are capacity-constrained.  No new refinery has
been built in the U.S. since 1976 and we have only half of the refineries we had
in 1981.

The combination of higher interest rates and higher energy prices leads us to
believe that economic growth will be a bit slower than the 4% we expected, but
we still expect growth around 3.5% in 2004 and 2005.

From Bancroft Convertible Fund's founding in 1971, the Fund's strategy has been
to use convertible securities as an equity alternative to reduce risk and
volatility.  This strategy tends to outperform in bear markets and lag in bull
markets.  The net asset value of the Fund has outperformed the S&P 500 stock
index for the five years ended April 30, 2004 and underperformed for the one
year ended April 30, 2004.  The nature of the Fund's convertible securities
investments explains much of this difference in performance during these
periods.  The Fund's NAV slightly underperformed the average of its peer-group
for the four months ended April 30, 2004.  Our peers consist of the thirteen
closed-end convertible funds in the Lipper Closed-End Performance Analysis, but
of these thirteen only four of these, including Bancroft, remain unleveraged
convertible funds with greater than 80% of their investments in convertible
securities.  The addition of leverage usually makes portfolios more volatile and
the addition of non-convertible debt increases exposure to interest rate risk.

The results of the 2004 annual shareholders' meeting are shown in the
Miscellaneous Notes section of this report.  We thank you for your participation
and support.  Additional information on the Fund is available on the Fund's
website (www.bancroftfund.com).  Further, shareholders who wish to obtain a copy
of the most recent report on the Fund issued by Standard and Poor's should
contact us.

At its May meeting, the Fund's Board of Directors declared a quarterly dividend
of 17 cents per share.  The dividend consists of undistributed net investment
income and will be payable  on June 29, 2004 to shareholders of record on
June 15, 2004.

/s/ Thomas H. Dinsmore
Thomas H. Dinsmore
Chairman of the Board

June 14, 2004
                                       1
<PAGE>

BANCROFT CONVERTIBLE FUND

Largest Investment Holdings by underlying common stock

<TABLE>
<CAPTION>
                                                                                      Value        % of Total
                                                                                     (Note 1)      Net Assets
                                                                                    -----------    ----------
<S>                                                                                <C>               <C>
Teva Pharmaceutical Industries Ltd. .............................................   $ 3,114,000       2.7%
  Develops, manufactures and markets generic and branded human
  pharmaceuticals and active pharmaceutical ingredients.

Amerada Hess Corp. ..............................................................     2,691,600       2.3
  The Company and its subsidiaries explore for, produce, purchase, transport and
  sell crude oil and natural gas. The Company also manufactures, purchases,
  transports and markets refined petroleum products.

Washington Mutual, Inc. .........................................................     2,486,250       2.2
  A financial services company that provides a diversified line of products
  and services to consumers and small to mid-sized businesses.

Church & Dwight Co., Inc. .......................................................     2,484,280       2.2
  Produces sodium bicarbonate and sodium bicarbonate-based products
  The Company sells its products primarily under the Arm & Hammer
  trademark, to consumers and to industrial customers and distributors.

The St. Paul Travelers Companies, Inc. ..........................................     2,457,000       2.1
  Provides a broad range of insurance products and services for the
  commercial and consumer markets.

Sovereign Bancorp, Inc. .........................................................     2,350,000       2.0
  A holding company for Sovereign Bank. The Bank's primary business
  consists of attracting deposits from its network of banking offices, and
  originating commercial, consumer and residential mortgage loans, as
  well as automobile loans.

Conexant Systems, Inc. ..........................................................     2,227,973       1.9
  Provides semiconductor products for communications electronics. The
  Company offers products for use in wireless communications, network
  access, network processing, digital entertainment, personal imaging, and
  personal computing.

Capital One Financial Corp. .....................................................     2,213,100       1.9
  Through its subsidiaries, provides credit card products, consumer lending
  and deposit services.

The TJX Companies, Inc. .........................................................     2,112,000       1.8
  Retails off-price apparel and home fashions. The Company currently
  operates T.J. Maxx, Marshalls, HomeGoods, A.J. Wright, Winners and
  T.K. Maxx stores.

Fifth Third Bancorp .............................................................     2,059,714       1.8
                                                                                    -----------      ----
  A diversified financial services company. The Company's principal businesses
  include retail banking, commercial banking, investment advisory and data
  processing.

                                                                                    $24,195,917      20.9%
                                                                                    ===========      ====
</TABLE>

                                       2
<PAGE>

BANCROFT CONVERTIBLE FUND

Major Industry Exposure

<TABLE>
<CAPTION>
                                                                     % of Total
                                                                     Net Assets
                                                                     ----------
<S>                                                                     <C>
Pharmaceuticals ...................................................     11.7%
Technology ........................................................     11.2
Banking/Savings & Loan ............................................     11.0
Financial & Insurance .............................................     10.7
Energy ............................................................     10.0
Retail ............................................................      7.9
Telecommunications ................................................      7.1
Health Care .......................................................      5.0
Automotive ........................................................      3.8
Consumer Goods ....................................................      3.5
                                                                       ------
Total .............................................................     81.9%
                                                                       ======
</TABLE>

Major Portfolio Changes
Six months ended April 30, 2004

<TABLE>
<CAPTION>
ADDITIONS                                                         REDUCTIONS
<S>                                                               <C>
Amerada Hess Corp.                                                Affiliated Computer Services, Inc.

Casual Male Retail Group, Inc.                                    American Electric Power Company, Inc.

Chesapeake Energy Corp.                                           Bisys Group, Inc.

                                                                  ChevronTexaco Corp.
Conexant Systems, Inc.                                             (exchangeable from Devon Energy Corp.)

EMC Corp.                                                         Equinix, Inc.
 (exchangeable from The Goldman Sachs Group, Inc.)
                                                                  Graftech International, Ltd.
Equinix, Inc.
                                                                  The Interpublic Group of Companies, Inc.
Fifth Third Bancorp
 (exchangeable from The Bear Stearns Cos., Inc.)                  Ivax Corp.

Graftech International, Ltd.                                      News Corp, Inc.
                                                                   (exchangeable from News America, Inc.)
Hewlett Packard Co., Inc.
                                                                  Nextel Communications, Inc.

LSI Logic Corp.                                                   Raytheon Co.
 (exchangeable from Lehman Brothers Holdings, Inc.)                (exchangeable from RC Trust I)

Leucadia National Corp.                                           Reinsurance Group of America, Inc.

Nortel Networks Corp.                                             School Specialty Inc.

Sovereign Bancorp, Inc.                                           Sunrise Assisted Living, Inc.
 (exchangeable from Sovereign Capital Trust IV)

The TJX Companies, Inc.                                           Toys "R" Us, Inc.

Teva Pharmaceuticals Industries Ltd.                              Vishay Intertechnology, Inc.
 (exchangeable from Teva Pharm. Finance II)

                                                                  XL Capital, Ltd.
</TABLE>

                                       3
<PAGE>

BANCROFT CONVERTIBLE FUND

Statement of Assets and Liabilities (unaudited)

<TABLE>
<CAPTION>
                                                                  April 30,2004
                                                                  -------------
Assets:
<S>                                                               <C>
   Investments at value (cost $111,282,870) (Note 1) ............  $115,597,141
   Cash .........................................................        90,763
   Receivable for securities sold ...............................       661,062
   Dividends and interest receivable ............................       542,652
   Other assets .................................................        48,458
                                                                   ------------
   Total assets .................................................   116,940,076
                                                                   ------------
Liabilities:
   Payable for securities purchased .............................     1,305,000
   Accrued management fee (Note 2) ..............................      72,200
   Accrued expenses .............................................        10,366
                                                                   ------------
   Total liabilities ............................................     1,387,566
                                                                   ------------
   Net Assets ...................................................  $115,552,510
                                                                   ============
Net assets consist of:
   Undistributed net investment income ..........................  $    879,875
   Accumulated net realized loss from investment transactions ...    (5,723,488)
   Unrealized appreciation on investments .......................     4,314,271
   Capital shares (Note 3) ......................................        55,568
   Additional paid-in capital ...................................   116,026,284
                                                                   ------------
Net Assets ......................................................  $115,552,510
                                                                   ============
Net asset value per share
($115,552,510 / 5,557,138 outstanding shares) ...................  $      20.79
                                                                   ============
</TABLE>

Statement of Operations (unaudited)
Six Months Ended April 30, 2004

<TABLE>
<S>                                                                <C>
Investment Income (Note 1):
  Interest ......................................................  $  1,317,258
  Dividends .....................................................     1,145,172
                                                                   ------------
    Total Income ................................................     2,462,430
                                                                   ------------
Expenses (Note 2):
  Management fee ................................................       408,973
  Custodian .....................................................        11,287
  Transfer agent ................................................        12,446
  Professional fees .............................................        37,678
  Directors' fees ...............................................        54,300
  Reports to shareholders .......................................        22,131
  Treasurer's office ............................................        12,500
  Other .........................................................        56,379
                                                                   ------------
     Total Expenses .............................................       615,694
                                                                   ------------
Net Investment Income ...........................................     1,846,736
                                                                   ------------
Realized and Unrealized Gain on Investments:
  Net realized gain from investment transactions ................     2,507,359
  Net unrealized depreciation of investments ....................       (28,245)
                                                                   ------------
  Net gain on investments .......................................     2,479,114
                                                                   ------------
  Net Increase in Net Assets Resulting from Operations ..........  $  4,325,850
                                                                   ============
</TABLE>

                See accompanying notes to financial statements.


                                       4
<PAGE>

BANCROFT CONVERTIBLE FUND

Statement of Changes in Net Assets

<TABLE>
<CAPTION>
                                                                  Six Months Ended       Year Ended
                                                                  April 30, 2004(a)    October 31, 2003
                                                                  -----------------    ----------------
<S>                                                                <C>                   <C>
Change in net assets from operations:
  Net investment income .........................................  $  1,846,736          $ 3,352,240
  Net realized gain (loss) from investment transactions .........     2,507,359             (424,570)
  Net change in unrealized appreciation of investments ..........       (28,245)          11,355,567
                                                                   ------------          -----------
    Net increase in net assets resulting from operations ........     4,325,850           14,283,237
                                                                   ------------          -----------
Dividends to shareholders from:
  Net investment income .........................................    (1,937,144)          (3,445,042)

Capital share transactions (Note 3)
  Value of shares issued on reinvestment of distributions .......       628,542              742,900
  Net proceeds from rights offering .............................    14,049,762                   --
                                                                   ------------          -----------
    Total capital share transactions ............................    14,678,304              742,900
                                                                   ------------          -----------
Change in net assets ............................................    17,067,010           11,581,095
Net assets at beginning of period ...............................    98,485,500           86,904,405
                                                                   ------------          -----------
Net assets at end of period (including undistributed net
investment income of $879,875 and $985,125, respectively) .......  $115,552,510          $98,485,500
                                                                   ============          ===========
</TABLE>

Financial Highlights Selected data for a share of common stock outstanding

<TABLE>
<CAPTION>
                                                Six Months
                                                  Ended                       Years Ended October 31,
                                                  April,        -----------------------------------------------------
                                                  2004(a)         2003       2002       2001       2000        1999
                                                 --------       -------    -------    -------    --------    --------
<S>                                              <C>            <C>        <C>        <C>        <C>         <C>
Operating Performance:
Net asset value, beginning of period .........   $  20.84       $ 18.55    $ 20.72    $ 27.09    $  27.35    $  26.89
                                                 --------       -------    -------    -------    --------    --------
Net investment income ........................       0.33          0.71       0.79       1.07        1.04        0.78
Net realized and unrealized gain (loss) ......       0.50          2.31      (2.02)     (3.23)       2.29        3.40
                                                 --------       -------    -------    -------    --------    --------
  Total from investment operations ...........       0.83          3.02      (1.23)     (2.16)       3.33        4.18
Less Distributions:
Dividends from net investment income .........      (0.38)        (0.73)     (0.94)     (1.11)      (0.80)      (0.78)
Distributions from realized gains ............         --            --         --      (3.10)      (2.90)      (2.94)
                                                 --------       -------    -------    -------    --------    --------
  Total distributions ........................      (0.38)        (0.73)     (0.94)     (4.21)      (3.70)      (3.72)
Capital Share Transactions:
Effect of rights offering ....................      (0.50)           --         --         --          --          --
Capital share repurchases ....................         --            --         --         --        0.11          --
                                                 --------       -------    -------    -------    --------    --------
  Total capital share transactions ...........      (0.50)           --         --         --        0.11          --
                                                 --------       -------    -------    -------    --------    --------
Net asset value, end of period ...............   $  20.79       $ 20.84    $ 18.55    $ 20.72    $  27.09    $  27.35
                                                 ========       =======    =======    =======    ========    ========
Market value, end of period ..................   $  18.35       $ 19.70    $ 17.54    $ 18.75    $  22.63    $  22.25

Total Net Asset Value Return (%)(b) ..........       1.58         16.67      (6.29)     (8.68)      13.62       16.36
Total Investment Return (%)(c) ...............      (4.99)        16.71      (1.82)      1.31       20.63       (2.96)

Ratios/Supplemental Data:
Net assets, end of period (in thousands) .....   $115,553       $98,486    $86,904    $95,864    $111,336    $103,791
Ratio of expenses to average net assets (%) ..        1.1(d)        1.2        1.2        1.1         1.1         1.1
Ratio of net investment income to
  average net assets (%) .....................        3.3(d)        3.6        4.0        4.9         3.8         3.0
Portfolio turnover rate (%) ..................         45            87         78         83          93          72
</TABLE>

(a)  Unaudited.
(b)  Assumes valuation of the Fund's shares, and reinvestment of dividends, at
     net asset values.
(c)  Assumes valuation of the Fund's shares at market price and reinvestment of
     dividends at actual reinvestment price.
(d)  Annualized.

                See accompanying notes to financial statements.


                                       5
<PAGE>

BANCROFT CONVERTIBLE FUND

Portfolio of Investments April 30, 2004 (unaudited)

<TABLE>
<CAPTION>
Principal                                                                                           Value
 Amount                                                                                            (Note 1)
-----------                                                                                      -----------
              CONVERTIBLE BONDS AND NOTES -- 53.6%

<S>           <C>                                                                               <C>
              Advertising -- 0.9%
$ 1,000,000   Lamar Advertising Company 2.875% 2010 cv. sub. notes (B2) ......................   $ 1,078,125
                                                                                                 -----------
              Aerospace and Defense -- 1.2%
  1,500,000   The Goldman Sachs Group, Inc. 1% 2009 exch. equity-linked notes (Aa3)
              (exch. for General Dynamics Corp. common stock) (1) ............................     1,438,740
                                                                                                 -----------
              Automotive -- 2.5%
  1,000,000   American Axle & Manufacturing Holdings, Inc. 2% 2024 cv. sr. notes (Baa3)
              (Acquired 02/06/04 - 02/12/04; Cost $1,044,500) (1) (2) ........................     1,010,625
  3,500,000   Lear Corp. 0% 2022 cv. sr. notes (Ba1) .........................................     1,826,563
                                                                                                 -----------
                                                                                                   2,837,188
                                                                                                 -----------
              Banking/Savings and Loan -- 1.8%
  2,078,000   The Bear Stearns Companies, Inc. 0.25% 2010 medium term notes (A1)
              (exch. for Fifth Third Bancorp common stock) (1) ...............................     2,059,714
                                                                                                 -----------
              Consumer Goods -- 2.2%
  2,000,000   Church & Dwight Co., Inc. 5.25% 2033 cv. sr. deb. (B1) .........................     2,484,280
                                                                                                 -----------
              Data-Processing Services -- 1.2%
  1,500,000   Pegasus Solutions, Inc. 3.875% 2023 cv. sr. notes (NR) .........................     1,387,500
                                                                                                 -----------
              Electrical Supplies -- 0.8%
  1,000,000   Graftech International LTD 1.625% 2024 cv. sr. deb. (B2)
              (Acquired 04/22/04; Cost $999,375) (2) .........................................       883,750
                                                                                                 -----------
              Energy -- 1.7%
  1,900,000   Kerr-McGee Corp. 5.25% 2010 cv. sub. deb. (Baa3) ...............................     2,006,457
                                                                                                 -----------
              Entertainment -- 1.0%
  1,250,000   Citadel Broadcasting Corp. 1.875% 2011 cv. sub. notes (NR)
              (Acquired 02/11/04 - 02/25/04; Cost $1,246,250) (2) ............................     1,201,563
                                                                                                 -----------
              Financial and Insurance -- 1.9%
  1,250,000   Leucadia National Corp. 3.75% 2014 cv. sr. sub. notes (Ba3)
              (Acquired 04/22/04; Cost $1,265,000) (2) .......................................     1,270,313
  1,000,000   Swiss Re America Holding Corp. 3.25% 2021 euro. sub. cv. bonds (Aa1)
              (conv. into Swiss Reinsurance Company common stock) (Acquired 11/15/01 -
              12/05/01; Cost $1,007,750) (2) .................................................       945,625
                                                                                                 -----------
                                                                                                   2,215,938
                                                                                                 -----------
              Health Care -- 3.4%
  1,000,000   AmerisourceBergen Corp. 5% 2007 cv. sub. notes (B1) ............................     1,177,950
  1,000,000   Community Health Systems, Inc. 4.25% 2008 cv. sub. notes (B3) ..................     1,064,100
    500,000   LifePoint Hospitals, Inc. 4.50% 2009 cv. sub. notes (B3) .......................       525,000
    125,000   Matria Healthcare, Inc. 4.875% 2024 cv. sr. sub. notes (NR)
              (Acquired 04/30/04; Cost $125,000) (2) .........................................       126,094
    875,000   Mentor Corp. 2.75% 2024 cv. sub. notes (NR)
              (Acquired 12/17/03 - 01/30/04; Cost $941,250) (2) ..............................     1,095,938
                                                                                                 -----------
                                                                                                   3,989,082
                                                                                                 -----------
</TABLE>

                                       6
<PAGE>

BANCROFT CONVERTIBLE FUND

Portfolio of Investments April 30, 2004 (continued)
<TABLE>
<CAPTION>
 Principal                                                                                         Value
  Amount                                                                                          (Note 1)
-----------                                                                                     -----------
              CONVERTIBLE BONDS AND NOTES -- (continued)
<S>           <C>                                                                               <C>
              Office Equipment -- 1.6%
$ 1,750,000   IOS Capital, LLC 5% 2007 cv. sub. notes (Ba3) (exch. for IKON Office Solutions,
              Inc. common stock) (Acquired 05/08/02 - 06/02/03; Cost $1,746,250) (2) ........   $ 1,828,750
                                                                                                -----------
              Pharmaceuticals -- 10.2%
  2,000,000   Alza Corp. 0% 2020 cv. sub. deb. (Aa1)
              (exch. for Johnson & Johnson common stock) ....................................     1,507,500
  2,000,000   Amgen, Inc. 0% 2032 LYONs (A2) (1) ............................................     1,478,973
  1,250,000   Gilead Sciences, Inc. 2% 2007 cv. sr. notes (NR) ..............................     1,744,531
  1,125,000   Impax Laboratories, Inc. 1.25% 2024 cv. sr. sub. deb. (NR)
              (Acquired 03/31/04 - 04/23/04; Cost $1,208,750) (2) ...........................     1,157,614
    500,000   Ivax Corp. 4.50% 2008 cv. sr. sub. notes (NR) .................................       506,250
  1,250,000   Ivax Corp. 1.50% 2024 cv. sr. notes (NR)
              (Acquired 02/27/04; Cost $1,262,103) (1) (2) ..................................     1,233,088
  1,050,000   Medarex, Inc. 2.25% 2011 cv. sr. notes (NR)
              (Acquired 04/27/04 - 04/28/04; Cost $1,055,000) (2) ...........................     1,031,625
    750,000   Teva Pharmaceutical Finance B.V. 0.75% 2021 cv. sub. deb. (BBB)
              (exch. for ADR representing Teva Pharmaceuticals Industries Ltd. common stock)      1,085,250
  1,000,000   Teva Pharmaceutical Finance II, LLC series A 0.50% 2024 cv. sr. deb. (BBB)
              (exch. for ADR representing Teva Pharmaceuticals Industries Ltd. common stock)      1,010,000
  1,000,000   Teva Pharmaceutical Finance II, LLC series B 0.25% 2024 cv. sr. deb. (BBB)
              (exch. for ADR representing Teva Pharmaceuticals Industries Ltd. common stock)      1,018,750
                                                                                                -----------
                                                                                                 11,773,581
                                                                                                -----------
              Retail -- 7.9%
  1,300,000   Dick's Sporting Goods, Inc. 1.6061% 2024 sr. cv. notes (NR)
              (Acquired 02/11/04 - 03/15/04; Cost $917,772) (2) .............................       882,375
  1,000,000   Casual Male Retail Group, Inc. 5% 2024 cv. sr. sub. notes (NR)
              (Acquired 11/13/03 - 12/19/03; Cost $1,015,985) (2) ...........................     1,165,000
  1,500,000   Charming Shoppes, Inc. 4.75% 2012 sr. cv. notes (B2) ..........................     1,629,375
  1,500,000   Costco Wholesale Corp. 0% 2017 cv. sub. notes (A3) ............................     1,289,063
  1,000,000   Reebok International Ltd. 2% 2024 cv. deb. (BBB)
              (Acquired 04/27/04; Cost $1,004,375) (1) (2) ..................................     1,003,750
  1,000,000   Saks, Inc. 2% 2024 cv. sr. notes (Ba3)
              (Acquired 03/17/04 - 04/23/04; Cost $1,021,985) (2) ...........................     1,009,950
  2,400,000   The TJX Companies, Inc. 0% 2021 LYONs (Baa1) ..................................     2,112,000
                                                                                                -----------
                                                                                                  9,091,513
                                                                                                -----------
              Technology -- 7.8%
  1,500,000   Axcelis Technologies, Inc. 4.25% 2007 cv. sub. notes (NR) .....................     1,488,750
  2,191,000   Conexant Systems, Inc. 5.25% 2006 cv. sub. notes (NR) .........................     2,227,973
  2,378,000   Hewlett-Packard Co., Inc. 0% 2017 LYONs (Baa1) ................................     1,331,680
  2,000,000   International Rectifier Corp. 4.25% 2007 cv. sub. notes (B2) ..................     2,002,500
  2,000,000   STMicroelectronics, N.V. 0% 2013 sr. cv. bonds (A3)
              (Acquired 07/29/03 - 12/22/03; Cost $2,067,500) (2) (3) .......................     1,980,000
                                                                                                -----------
                                                                                                  9,030,903
                                                                                                -----------
</TABLE>

                                       7
<PAGE>

BANCROFT CONVERTIBLE FUND

Portfolio of Investments April 30, 2004 (continued)

<TABLE>
<CAPTION>
 Principal                                                                                         Value
  Amount                                                                                          (Note 1)
-----------                                                                                     -----------
              CONVERTIBLE BONDS AND NOTES -- (continued)

              Telecommunications -- 7.1%
<S>           <C>                                                                                     <C>
 $1,500,000   Comverse Technology, Inc. 0% 2023 ZYPS (BB-) (3) ..............................   $ 1,706,250
  1,000,000   Lucent Technologies, Inc. 2.75% 2023 series A cv. sr. deb. (Caa1) .............     1,293,340
    500,000   Lucent Technologies, Inc. 2.75% 2025 series B cv. sr. deb. (Caa1) .............       674,950
    500,000   NII Holdings, Inc. 2.875% 2034 cv. sr. notes (NR)
              (Acquired 01/27/04; Cost $510,313) (2) ........................................       519,369
  1,250,000   Nortel Networks Corp. 4.25% 2008 cv. sr. notes (B3) ...........................     1,176,563
  1,250,000   Tekelec, Inc. 2.25% 2008 cv. sub. discount notes (NR) .........................     1,490,625
  1,000,000   UTStarcom, Inc. 0.875% 2008 cv. notes (NR) ....................................     1,308,750
                                                                                                -----------
                                                                                                  8,169,847
                                                                                                -----------
              Transportation -- 0.4%
    500,000   ExpressJet Holdings, Inc. 4.25% 2023 cv. notes (NR) ...........................       510,480
                                                                                                -----------
              TOTAL CONVERTIBLE BONDS AND NOTES .............................................    61,987,411
                                                                                                -----------
<CAPTION>
  Shares
-----------
<S>           <C>                                                                               <C>
              CONVERTIBLE PREFERRED STOCKS -- 20.2%

              Automotive -- 1.3%
     50,000   General Motors Corp. 6.25% series C cv. sr. deb. (Baa1) .......................     1,515,625
                                                                                                -----------
              Banking/Savings and Loan -- 8.2%
     20,000   Commerce Capital Trust II 5.95% cv. trust pfd. (Baa1)
              (exch. for Commerce Bancorp, Inc. common stock) ...............................     1,237,500
     40,000   National Australia Bank Ltd. 7.875% exch. capital units (NR) ..................     1,436,400
     30,000   New York Community Bancorp, Inc. 6% BONUSES units (Baa2) ......................     1,987,500
     50,000   Sovereign Capital Trust IV 4.375% PIERS (Ba1)
              (exch. for Sovereign Bancorp, Inc. common stock) (1) ..........................     2,350,000
     45,000   Washington Mutual Capital Trust PIERS units (Baa1)
              (exch. for Washington Mutual, Inc. common stock) ..............................     2,486,250
                                                                                                -----------
                                                                                                  9,497,650
                                                                                                -----------
              Energy -- 2.9%
     12,500   Chesapeake Energy Corp. 6% cum. cv. pfd. (B3) .................................       942,972
      1,000   Chesapeake Energy Corp. 4.125% cum. cv. pfd. (B3)
              (Acquired 03/24/04; Cost $1,000,000) (2) ......................................     1,048,750
     20,000   The Williams Companies, Inc. 5.50% 2033 jr. sub. cv. deb. (B-) ................     1,347,500
                                                                                                -----------
                                                                                                  3,339,222
                                                                                                -----------
              Entertainment -- 2.3%
     22,500   Emmis Communications Corp. 6.25% series A cum. cv. pfd. (Caa1) ................     1,065,938
      1,500   Radio One, Inc. 6.50% HIGH TIDES (B3) .........................................     1,615,500
                                                                                                -----------
                                                                                                  2,681,438
                                                                                                -----------
              Financial and Insurance -- 3.1%
     20,000   Reinsurance Group of America, Inc. 5.75% PIERS (Baa2) .........................     1,148,500
    100,000   The St. Paul Travelers Companies, Inc. 4.50% 2032 cv. jr. sub. notes (Baa1) ...     2,457,000
                                                                                                -----------
                                                                                                  3,605,500
                                                                                                -----------
              Health Care -- 1.6%
     29,000   Omnicare Capital Trust I 4% PIERS (Ba3)
              (exch. for Omnicare, Inc. common stock) (1) ...................................     1,798,000
                                                                                                -----------
              Mining -- 0.8%
      1,000   Freeport-McMoRan Copper and Gold, Inc. 5.50% cv. perpetual pfd. (CCC) .........       882,750
                                                                                                -----------
              TOTAL CONVERTIBLE PREFERRED STOCKS ............................................    23,320,185
                                                                                                -----------
</TABLE>


                                       8
<PAGE>

BANCROFT CONVERTIBLE FUND

Portfolio of Investments April 30, 2004 (continued)

<TABLE>
<CAPTION>
Principal
 Amount                                                                                            Value
or Shares                                                                                         (Note 1)
-----------                                                                                     -----------
<S>            <C>                                                                               <C>
               MANDATORY CONVERTIBLE SECURITIES-- 21.6% Note 1(e)

               Aerospace and Defense -- 1.3%
    15,000 shs Northrop Grumman Corp. 7.25% equity units (NR) (1) ............................   $ 1,569,450
                                                                                                 -----------
               Banking/Savings and Loan -- 1.0%
     5,000 shs State Street Corp. 6.75% treasury backed ACES (NR) ............................     1,159,219
                                                                                                 -----------
               Consumer Goods -- 1.3%
    50,000 shs Constellation Brands, Inc. dep. shs.
                representing 5.75% series A mand. cv. pfd. (B) ...............................     1,532,000
                                                                                                 -----------
               Energy -- 5.3%
    40,000 shs Amerada Hess Corp.7% mandatory cv. pfd. ACES (Ba3) ............................     2,691,600
    30,000 shs Kerr-McGee Corp. 5.50% 2004 DECS (Baa3)
               (exch. for Devon Energy Corp. common stock) ...................................     1,565,700
    25,000 shs Teekay Shipping Corp. 7.25% PEPS units (BB-) ..................................       935,250
    30,000 shs Valero Energy Corp. 2% mandatory cv. pfd. (BB+) ...............................       971,520
                                                                                                 -----------
                                                                                                   6,164,070
                                                                                                 -----------
               Financial and Insurance -- 5.7%
    45,000 shs Capital One Financial Corp. 6.25% Upper DECS (Baa3) (1) .......................     2,213,100
    15,000 shs The Chubb Corp. 7% equity units (A) (1) .......................................       420,000
    54,000 shs The Chubb Corp. 7% equity units (A) (1) .......................................     1,508,625
    40,000 shs Platinum Underwriters Holdings, Ltd. 7% equity security units (NR) (1) ........     1,298,000
    45,000 shs XL Capital, Ltd. 6.5% equity security units (A2) ..............................     1,141,875
                                                                                                 -----------
                                                                                                   6,581,600
                                                                                                 -----------
               Paper and Paper Products -- 1.0%
    20,000 shs Temple-Inland, Inc. 7.50% Upper DECS (Baa3) (1) ...............................     1,122,000
                                                                                                 -----------
               Pharmaceuticals -- 1.5%
    31,500 shs Baxter International, Inc. 7% equity units (A3) (1) ...........................     1,700,055
                                                                                                 -----------
               Technology -- 3.4%
   105,550 shs The Goldman Sachs Group, Inc. 7.50% mandatory exch. notes (Aa3)
               (exch. for EMC Corp. common stock) ............................................     1,268,342
    36,395 shs The Goldman Sachs Group, Inc. 5.625% mandatory exch. notes (Aa3)
               (exch. for Intel Corp. common stock) ..........................................       952,130
$2,000,000     Lehman Brothers Holdings, Inc. 6% 2005 YEELDS (A)
               (linked to LSI Logic Corp. common stock) ......................................     1,672,500
                                                                                                 -----------
                                                                                                   3,892,972
                                                                                                 -----------
               Utilities -- 1.1%
    50,000 shs DTE Energy Co. 8.75% equity security units (BBB) (1) ..........................     1,234,500
                                                                                                 -----------
               TOTAL MANDATORY CONVERTIBLE SECURITIES Note 1(e) ..............................    24,955,866
                                                                                                 -----------
               COMMON STOCKS -- 0.0%

               Telecommunications -- 0.0%
    11,743 shs Covad Communications Group, Inc. (3) ..........................................        23,486
                                                                                                 -----------
               TOTAL COMMON STOCKS ...........................................................        23,486
                                                                                                 -----------
</TABLE>


                                       9
<PAGE>

BANCROFT CONVERTIBLE FUND

Portfolio of Investments April 30, 2004 (continued)

<TABLE>
<CAPTION>
 Principal                                                                                        Value
  Amount                                                                                         (Note 1)
-----------                                                                                    ------------
<S>           <C>                                                                              <C>
              SHORT-TERM SECURITIES -- 4.6%

              Commercial Paper -- 4.6%
$2,900,000    American Express Credit Corp. (P1)
              (0.99% maturing 05/03/04)......................................................  $  2,899,601
 2,400,000    American Express Credit Corp. (P1)
              (1.02% maturing 05/06/04)......................................................     2,399,592
                                                                                               ------------
                                                                                                  5,299,193
                                                                                               ------------
              U.S. Government Obligations -- 0.0%
    11,000    U.S. Treasury notes 1.625% 4/30/05 (Aaa) (4)...................................        11,000
                                                                                               ------------
              TOTAL SHORT-TERM SECURITIES....................................................     5,310,193
                                                                                               ------------
              Total Investments -- 100.0%....................................................   115,597,141
              Other assets and liabilities, net -- (0.0)%....................................       (44,631)
                                                                                               ------------
              Total Net Assets -- 100.0%.....................................................  $115,552,510
                                                                                               ============
</TABLE>


(1)  Contingent payment debt instrument which accrues contingent interest
     income. See Note 1(b).

(2)  Security not registered under the Securities Act of 1933, as amended (e.g.,
     the security was purchased in a Rule 144A transaction or a Regulation D
     transaction). The security may be resold only pursuant to an exemption from
     registra- tion under the 1933 Act, typically to qualified institutional
     buyers. The Fund generally has no rights to demand registration of these
     securities. The aggregate market value of these securities at April 30,
     2004 was $19,394,179, which represented 16.8% of the Fund's net assets.

(3)  Non-income producing security.

(4)  Collateral for a letter of credit.

ACES         Automatic Convertible Equity Securities.
ADR          American Depositary Receipts.
BONUSES      Bifurcated Option Note Unit Securities.
DECS         Debt Exchangeable for Common Stock.
HIGH TIDES   Remarketable Term Income Deferrable Equity Securities.
LYONs        Liquid Yield Option Notes.
PEPS         Premium Equity Particpating Securities.
PIERS        Preferred Income Equity Redeemable Securities.
YEELDS       Yield Enhanced Equity Linked Debt Securities.
ZYPS         Zero Yield Puttable Securities.

Ratings in parentheses by Moody's Investors Service, Inc. or Standard & Poor's,
a division of McGraw-Hill Companies. NR is used whenever a rating is
unavailable.

The cost of investments for federal income tax purposes is $111,282,870
resulting in gross unrealized appreciation and depreciation of $7,264,619 and
$2,950,348, respectively, or net unrealized appreciation of $4,314,271 on a tax
cost basis.

The Fund invests primarily in convertible securities. Some convertible
securities the Fund invests in may be "restricted securities." Typically,
securities are considered "restricted securities" when they are not registered
under the Securities Act of 1933, as amended (the "Securities Act") and may be
resold only pursuant to an exemption from registration under the Securities Act.

                See accompanying notes to financial statements.

                                       10
<PAGE>


BANCROFT CONVERTIBLE FUND

Notes to Financial Statements (unaudited)

1.  Significant Accounting Policies
Bancroft Convertible Fund, Inc. (the "Fund") is registered under the Investment
Company Act of 1940 as a diversified, closed-end management investment company.
The preparation of financial statements in conformity with generally accepted
accounting principles requires management to make estimates and assumptions that
affect the reported amounts of assets and liabilities at the date of the
financial statements, and the reported amounts of revenue and expenses during
the reporting period. Actual results could differ from those estimates. The
following is a summary of significant accounting policies consistently followed
by the Fund in the preparation of its financial statements:

(a)  Security Valuation
Investments in securities traded on a national securities exchange are valued at
market using the last reported sales price as of the close of regular trading.
Unlisted securities traded in the over-the-counter market and listed securities
for which no sales were reported, are valued at the mean between closing
reported bid and asked prices as of the close of regular trading. Securities for
which quotations are not readily available, restricted securities and other
assets are valued at fair value as determined in good faith by management with
the approval of the Board of Directors. Short-term debt securities with initial
maturities of 60 days or less are valued at amortized cost.

(b)  Securities Transactions and Related Investment Income
Security transactions are accounted for on the trade date (date the order to buy
or sell is executed) with gain or loss on the sale of securities being
determined based upon identified cost. Dividend income is recorded on the
ex-dividend date and interest income is recorded on the accrual basis, including
accretion of discounts and amortization of non-equity premium. For certain
securities, known as "contingent payment debt instruments," Federal tax
regulations require the Fund to record non-cash, "contingent" interest income in
addition to interest income actually received. Contingent interest income
amounted to 5 cents per share for the six months ended April 30, 2004.

(c)  Federal Income Taxes
It is the policy of the Fund to distribute substantially all of its taxable
income within the prescribed time and to otherwise comply with the provisions of
the Internal Revenue Code applicable to regulated investment companies.
Therefore, no provision for federal income or excise taxes is believed
necessary. At October 31, 2003, the net capital loss carryforward of the Fund
which may be used to offset possible future net realized gains was approximately
$8,230,848, and expires in 2009, 2010 and 2011.

(d)  Dividends and Distributions to Shareholders
The liability for dividends and distributions payable is recorded on the
ex-dividend date.

(e)  Market Risk
It is the Fund's policy, under normal circumstances, to invest at least 80% of
its assets in convertible securities. Although convertible securities do derive
part of their value from that of the securities into which they are convertible,
they are not considered derivative financial instruments. However, certain of
the Fund's investments include features which render them more sensitive to
price changes in their underlying securities. Thus they expose the Fund to
greater downside risk than traditional convertible securities, but still less
than that of the underlying common stock. At April 30, 2004, the market value of
those securities was $24,955,866, representing 21.6% of net assets.

2.  Management Fee and Other Transactions with Affiliates
The management fee is paid to the investment adviser, Davis-Dinsmore Management
Company (the "Adviser"). The contract provides for payment of a monthly advisory
fee, computed at an annual rate of 3/4 of 1% of the first $100,000,000 and 1/2
of 1% of the excess over $100,000,000 of the Fund's net asset value in such
month.

The Adviser invests the Fund's assets, furnishes office equipment and
facilities, and pays the salaries of all executive officers of the Fund, except
that the costs associated with personnel and certain non-personnel expenses of
the office of the Treasurer up to a maximum of $25,000 a year are reimbursed by
the Fund. Such reimbursements amounted to $12,500 for the six months ended April
30, 2004. The officers of the Fund are also directors, officers or employees of
the Adviser, and are compensated by the Adviser.


                                       11
<PAGE>

BANCROFT CONVERTIBLE FUND

Notes to Financial Statements (continued)

3.  Portfolio Activity
At April 30, 2004 there were 5,557,138 shares of $.01 par value common stock
outstanding (9,000,000 shares authorized). During the six months ended April 30,
2004, 33,362 shares were issued in connection with reinvestment of dividends
from net investment income, resulting in an increase in paid-in capital of
$628,542.

On December 16, 2003, the Fund completed a rights offering of Common Stock to
its stockholders at the rate of one common share for each 6 rights held by
stockholders of record on November 13, 2003. The rights offering was fully
subscribed, resulting in the issuance of 797,918 common shares at a price of
$17.82, and proceeds of $14,218,899 to the Fund prior to the deduction of
expenses. The net asset value per share of the Fund's Common Stock was reduced
by approximately $0.50 per share as a result of the issuance.

Purchases and sales of investments, exclusive of corporate short-term notes,
aggregated $58,698,124 and $48,431,018, respectively, for the six months ended
April 30, 2004.

A distribution of $0.17 per share from net investment income was declared on May
18, 2004, payable June 29, 2004 to shareholders of record at the close of
business June 15, 2004.

Miscellaneous Notes

Results of the 2004 Annual Shareholders Meeting

The results of the shareholder vote at the Annual Meeting of Shareholders held
on February 14, 2004, were:

1.   All directors nominated by management were elected for terms expiring in
     2007.

                                  Shares voted for             Shares withheld
                                  ----------------             ---------------
     Gordon F. Ahalt                 4,119,528                     112,509
     Nicolas W. Platt                4,119,832                     112,205
     Jane D. O'Keeffe                4,117,717                     114,320

2.   The Audit Committee's appointment of PricewaterhouseCoopers LLP as
     independent accountants was ratified with 4,158,991 shares voted for,
     34,785 shares voted against and 38,261 shares abstaining.
--------------------------------------------------------------------------------
Visit us on the Internet at www.bancroftfund.com. The site provides information
about the Fund including daily net asset values (NAV), historical dividends and
press releases, as well as information about Davis-Dinsmore Management Company,
the Fund's adviser. In addition you can send email to us at
info@bancroftfund.com.
--------------------------------------------------------------------------------
The Fund is a member of the Closed-End Fund Association (CEFA). The group's
website address is www.cefa.com. CEFA is solely responsible for the content of
its website.
--------------------------------------------------------------------------------
The Fund's Proxy Voting Guidelines (the "Guidelines") are available without
charge, by calling the Fund collect at (973) 631-1177. The Guidelines are also
posted on the Fund's web-site at http://www.bancroftfund.com and are available
on the SEC's website at http://www.sec.gov.
--------------------------------------------------------------------------------
Pursuant to Section 23 of the Investment Company Act of 1940, notice is hereby
given that the Fund may in the future purchase shares of its own common stock
from time to time, at such times, and in such amounts, as may be deemed
advantageous to the Fund. Nothing herein shall be considered a commitment to
purchase such shares.



                                       12
<PAGE>


<TABLE>
<CAPTION>
Board of Directors
<S>                                      <C>
GORDON F. AHALT                          Retired Petroleum Consultant
WILLIAM A. BENTON                        Retired Stock Exchange Specialist
ELIZABETH C. BOGAN, PH.D.                Senior Lecturer in Economics at Princeton University
THOMAS H. DINSMORE, C.F.A.               Chairman of the Board of the Fund
DONALD M. HALSTED, JR.                   Retired Business Executive
GEORGE R. LIEBERMAN                      Retired Advertising Executive
DUNCAN O. MCKEE                          Retired Attorney
JANE D. O'KEEFFE                         President of the Fund
NICOLAS W. PLATT                         Public Relations Executive

<CAPTION>
Officers
<S>                                      <C>
THOMAS H. DINSMORE                       Chief Executive Officer
JANE D. O'KEEFFE                         President
GARY I. LEVINE                           Executive Vice President, Chief Financial Officer and Secretary
H. TUCKER LAKE, JR.                      Vice President
GERMAINE M. ORTIZ                        Vice President
MERCEDES A. PIERRE                       Vice President and Assistant Treasurer
JOSHUA P. LAKE                           Treasurer and Assistant Secretary
JESSICA K. LAKE                          Assistant Vice President
JOANN VENEZIA                            Assistant Vice President
</TABLE>

--------------------------------------------------------------------------------

Internet
www.bancroftfund.com
email: info@bancroftfund.com

Investment Adviser
Davis-Dinsmore Management Company
65 Madison Avenue, Morristown, NJ 07960-7308
(973) 631-1177

Shareholder Services and Transfer Agent
American Stock Transfer & Trust Company
59 Maiden Lane
New York, NY 10038
(800) 937-5449
www.amstock.com

Common Stock Listing
American Stock Exchange Symbol: BCV
<PAGE>


                         BANCROFT CONVERTIBLE FUND, INC.
                          65 MADISON AVENUE, SUITE 550
                          MORRISTOWN, NEW JERSEY 07960
                              www.bancroftfund.com


                    [LOGO AMERICAN STOCK EXCHANGE LISTED BCV]


                    (Recycle Logo) Printed on recycled paper
<PAGE>

ITEM 2. CODE OF ETHICS.

Not applicable to this semi-annual report.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.

Not applicable to this semi-annual report.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.

Not applicable to this semi-annual report.

ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS.

Not applicable to this semi-annual report.

ITEM 6. SCHEDULE OF INVESTMENTS.

The Schedule of Investments in securities of unaffiliated issuers is included as
part of the report to shareholders, filed under Item 1 of this Form.

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
MANAGEMENT INVESTMENT COMPANIES.

Not applicable to this semi-annual report.

ITEM 8. PURCHASE OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT
COMPANY AND AFFILIATED PURCHASERS.

There were no purchases made by or on behalf of the registrant or any
"affiliated purchaser," as defined in Rule 10b-18(a)(3) under the Exchange Act
(17 CFR 240.10b-18(a)(3)), of shares or other units of any class of the
registrant's equity securities that is registered by the registrant pursuant to
Section 12 of the Exchange Act(15 U.S.C. 781).

ITEM 9. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

The registrant adopted Shareholder Communication Procedures (the "Procedures")
effective April 19, 2004.  The Procedures are intended to set forth the process
by which shareholders of the registrant may send communications to the Board.
If a shareholder sends a recommendation of a nominee to the Board or to an
individual director, such communication would be covered by the Procedures.
Shareholder proposals submitted pursuant to Rule 14a-8 under the Securities
Exchange Act of 1934, as amended (the "1934 Act"), and communications made in
connection with such proposals are not subject to the Procedures.  The
Registrant's Bylaws also contain provisions requiring a shareholder to provide
advance notice of his or her intention to nominate, at the Registrant's annual
meeting of shareholders, an individual for election as director.

Pursuant to the Procedures, shareholders should send their communications to the
Shareholder Relations Group.  Communications may be sent by regular mail or
delivery service to the following address: 65 Madison Avenue, Suite 550,
Morristown, NJ 07960.  E mail communications may be sent to:
info@bancroftfund.com.  All shareholder communications received by the
Shareholder Relations Group shall be promptly forwarded to the individual
director of the registrant to whom they were addressed or to the full Board, as
applicable.  Copies of all such shareholder communications will also be
distributed to the Chairs of each of the registrant's Audit Committee, and
Nominating and Administration Committee, and to counsel for the registrant and
for the independent directors.  Counsel for the registrant and for the
independent directors, upon receipt of its copy of a shareholder communication,
shall work with such Chairs and counsel for the independent directors to
determine whether such shareholder communication should be distributed to any
directors to whom it was not sent and whether and in what manner the directors
should respond to such shareholder communication.  Responses, if any, to
shareholder communications shall be coordinated by counsel for the registrant
and for the independent directors, working with the Chairs.

ITEM 10. CONTROLS AND PROCEDURES

Conclusions of principal officers concerning controls and procedures

(a) As of May 26, 2004, an evaluation was performed under the supervision and
with the participation of the officers of Bancroft Convertible Fund, Inc. (the
"Registrant"), including the Principal Executive Officer ("PEO") and Principal
Financial Officer ("PFO"), to assess the effectiveness of the Registrant's
disclosure controls and procedures, as that term is defined in Rule 30a-3(c)
under the Investment Company Act of 1940 (the "Act"), as amended. Based on that
evaluation, the Registrant's officers, including the PEO and PFO, concluded
that, as of May 26, 2004, the Registrant's disclosure controls and procedures
were reasonably designed so as to ensure: (1) that information required to be
disclosed by the Registrant on Form N-CSR is recorded, processed, summarized
and reported within the time periods specified by the rules and forms of the
Securities and Exchange Commission; and (2) that material information relating
to the Registrant is made known to the PEO and PFO as appropriate to allow
timely decisions regarding required disclosure.

(b) There have been no significant changes in the Registrant's internal control
over financial reporting (as defined in Rule 30a-3(d) under the Act
(17 CFR 270.30a-3(d)) that occurred during the Registrant's last fiscal half-
year (the Registrant's second fiscal half-year in the case of an annual report)
that has materially affected, or is reasonably likely to materially affect,
the Registrant's internal control over financial reporting.

ITEM 11. EXHIBITS

(a)(1) The code of ethics disclosure required by Item 2 is not applicable to
this semi-annual report.

(a)(2) Certifications of the principal executive officer and the principal
financial officer pursuant to Rule 30a-2(a) under the Investment Company Act
of 1940.

(a)(3) There were no written solicitations to purchase securities under Rule
23c-1 under the Investment Company Act of 1940 during the period covered by the
report.

(b) Certifications of the principal executive officer and the principal
financial officer, as required by Rule 30a-2(b) under the Investment Company Act
of 1940.

<PAGE>
SIGNATURES

  Pursuant to the requirements of the Securities and Exchange Act of 1934 and
the Investment Company Act of 1940, the registrant has duly caused this report
to be signed on its behalf by the undersigned, thereunto duly authorized.

Bancroft Convertible Fund, Inc.

By: /s/Thomas H. Dinsmore
    Thomas H. Dinsmore
    Chairman of the Board and
    Chief Executive Officer
    (Principal Executive Officer)

Date: June 28, 2004

  Pursuant to the requirements of the Securities and Exchange Act of 1934 and
the Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By: /s/Thomas H. Dinsmore
    Thomas H. Dinsmore
    Chairman of the Board and
    Chief Executive Officer
    (Principal Executive Officer)

Date: June 28, 2004

By: /s/Gary I. Levine
    Gary I. Levine
    Chief Financial Officer
    (Principal Financial Officer)

Date: June 28, 2004

<PAGE>
EXHIBIT INDEX

(a)(1) The code of ethics disclosure required by Item 2 is not applicable to
this semi-annual report.

(a)(2) Certifications of the principal executive officer and the principal
financial officer pursuant to Rule 30a-2(a) under the Investment Company Act
of 1940.

(a)(3) There were no written solicitations to purchase securities under Rule
23c-1 under the Investment Company Act of 1940 during the period covered by the
report.

(b) Certifications of the principal executive officer and the principal
financial officer, as required by Rule 30a-2(b) under the Investment Company Act
of 1940.

</TEXT>
</DOCUMENT>
