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 on Form 10-K of Unifi, Inc. (the “Company”) for the fiscal year ended June 30, 2019, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Thomas H. Caudle, Jr., President & Chief Operating 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 results of operations of the Company.

Date:	August 29, 2019	/s/ THOMAS H. CAUDLE, JR.
		Thomas H. Caudle, Jr. President & Chief Operating Officer (Principal Executive Officer)