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 Annual Report of Allegiance Bancshares, Inc. (the “Company”) on Form 10-K for the period ending December 31, 2015 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, George Martinez, Chairman and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 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 operating results 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 March 22, 2016.

/s/ George Martinez

George Martinez

Chairman and Chief Executive Officer