Fiesta Restaurant (FRGI) 10-Q 2016 Q1 Quarterly report

Exhibit 32.1

CERTIFICATE PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned, Timothy P. Taft, Chief Executive Officer of Fiesta Restaurant Group, Inc. (the “Company”), hereby certifies, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Company's Quarterly Report on Form 10-Q for the period ended April 3, 2016, as filed with the Securities and Exchange Commission on the date hereof (the “Quarterly Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/s/ TIMOTHY P. TAFT

Timothy P. Taft

Chief Executive Officer

May 9, 2016