Exhibit 32.1

Certification of Chief Executive Officer of Approach Resources Inc.

(Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002)

In connection with the Quarterly Report of Approach Resources Inc. (the “Company”) on Form 10-Q for the period ended September 30, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, J. Ross Craft, Chairman of the Board and Chief Executive Officer of the Company, hereby certify, pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

| (1) | The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

| (2) | The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

|  |  | APPROACH RESOURCES INC.
Date: | November 8, 2018 |  | /s/ J. Ross Craft
|  | J. Ross Craft
|  | Chairman of the Board and Chief Executive Officer
|  | (Principal Executive Officer)