Exhibit 32.1

CERTIFICATION 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 Independent Bank Group, Inc. (the “Company”) on Form 10-Q for the period ending September 30, 2016 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, David R. Brooks, Chairman, Chief Executive Officer and President of the Company, certify to my knowledge and in my capacity as an officer of the Company, pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

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 as of the dates and for the periods expressed in the Report.

IN WITNESS WHEREOF, the undersigned has executed this Certificate, effective as of October 27, 2016.

/s/ David R. Brooks

David R. Brooks

Chairman, Chief Executive Officer and President