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 Quarterly Report of CU BANCORP (the “Company”) on Form 10-Q for the quarter ending June 30, 2017 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, David I. Rainer, Chief Executive Officer of the Company, and Karen A. Schoenbaum, Chief Financial 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 to the best of our knowledge, based on a review of the Report of the Company, and except as corrected or supplemented in a subsequent report:

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