Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Pedro (Pete) P. Rodriguez, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report of Exar Corporation on Form 10-Q for the period ended September 27, 2009 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, and that the information contained in such Quarterly Report on Form 10-Q fairly presents in all material respects the financial condition and results of operations of Exar Corporation.

Date: November 5, 2009

/s/    PEDRO (PETE) P. RODRIGUEZ        

Pedro (Pete) P. Rodriguez

Chief Executive Officer, President and Director

(Principal Executive Officer)