HEI Exhibit 32.1

Hawaiian Electric Industries, Inc.

Certification Pursuant to

18 U.S.C. Section 1350

In connection with the Quarterly Report of Hawaiian Electric Industries, Inc. (HEI) on Form 10-Q for the quarter ended June 30, 2014, as filed with the Securities and Exchange Commission on the date hereof (the Report), we, Constance H. Lau and James A. Ajello, Chief Executive Officer and Chief Financial Officer, respectively, of HEI, certify, pursuant to 18 U.S.C. Section 1350, that to the best of our knowledge:

(1)   The Report fully complies with the requirements of section 13(a) 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 HEI and its subsidiaries as of, and for, the periods presented in this report.

Date: August 11, 2014

/s/ Constance H. Lau

Constance H. Lau

President and Chief Executive Officer

/s/ James A. Ajello

James A. Ajello

Executive Vice President and Chief Financial Officer

A signed original of this written statement has been provided to HEI and will be retained by HEI and furnished to the Securities and Exchange Commission or its staff upon request.