<SEC-DOCUMENT>0001209191-19-027285.txt : 20190503
<SEC-HEADER>0001209191-19-027285.hdr.sgml : 20190503
<ACCEPTANCE-DATETIME>20190503152329
ACCESSION NUMBER:		0001209191-19-027285
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20190502
FILED AS OF DATE:		20190503
DATE AS OF CHANGE:		20190503

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Okray Thomas B
		CENTRAL INDEX KEY:			0001689107

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-05684
		FILM NUMBER:		19795848

	MAIL ADDRESS:	
		STREET 1:		5008 AIRPORT ROAD NW
		CITY:			ROANOKE
		STATE:			VA
		ZIP:			24012

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			GRAINGER W W INC
		CENTRAL INDEX KEY:			0000277135
		STANDARD INDUSTRIAL CLASSIFICATION:	WHOLESALE-DURABLE GOODS [5000]
		IRS NUMBER:				361150280
		STATE OF INCORPORATION:			IL
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		100 GRAINGER PARKWAY
		CITY:			LAKE FOREST
		STATE:			IL
		ZIP:			60045-5201
		BUSINESS PHONE:		847-535-1000

	MAIL ADDRESS:	
		STREET 1:		100 GRAINGER PARKWAY
		CITY:			LAKE FOREST
		STATE:			IL
		ZIP:			60045
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000277135</issuerCik>
        <issuerName>GRAINGER W W INC</issuerName>
        <issuerTradingSymbol>GWW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001689107</rptOwnerCik>
            <rptOwnerName>Okray Thomas B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>100 GRAINGER PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LAKE FOREST</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60045</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1177</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>274.86</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7513</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>311.26</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2029-03-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>9355</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9355</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The stock option will fully vest in three years, where 1/3 shall vest on April 1, 2020, 1/3 shall vest on April 1, 2021, and the remainder shall vest on 4/1/2022.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Hugo Dubovoy, Jr., as attorney-in-fact</signatureName>
        <signatureDate>2019-05-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
