Exhibit 32.1

CERTIFICATION

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350, as adopted), Dr. Paramesh Gopi, Chief Executive Officer of Applied Micro Circuits Corporation (the “Company”), hereby certifies that, to the best of his knowledge:

1. This Quarterly Report on Form 10-Q for the quarterly period ended June 30, 2011 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”).

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

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission (“SEC”) or its staff upon request.

This certification accompanies the Report to which it relates, is not deemed filed with the SEC and is not to be incorporated by reference into any filing of the Company under the Securities Act of 1933, as amended, or the Exchange Act (whether made before or after the date of the Report), irrespective of any general incorporation language contained in such filing.

Dated: August 1, 2011