Exhibit 32.1

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER

UNDER

SECTION 906 OF THE SARBANES-OXLEY ACT

PACIFIC MERCANTILE BANCORP

Annual Report on Form 10-K

for the Year ended December 31, 2011

In connection with the accompanying Annual Report on Form 10-K of Pacific Mercantile Bancorp (the “Company”) for the fiscal year ended December 31, 2011 (the “Annual Report”), and pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2003, I, Raymond E. Dellerba, certify that:

(1) The Annual Report fully complies with the requirements of Section 13(a) and 15(d) of the Securities Exchange Act of 1934; and

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

Dated: February 24, 2012

/S/    RAYMOND E. DELLERBA        

Raymond E. Dellerba

President and Chief Executive Officer

A signed original of this written statement required by Section 906 has been provided to Pacific Mercantile Bancorp and will be retained by Pacific Mercantile Bancorp and furnished to the Securities and Exchange Commission or its staff upon request.