HEI Exhibit 32.1

Hawaiian Electric Industries, Inc.

Certificate Pursuant to

18 U.S.C. Section 1350

In connection with the Annual Report of Hawaiian Electric Industries, Inc. (HEI) on Form 10-K for the year ended December 31, 2012, as filed with the Securities and Exchange Commission (the Report), each of 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 her or his knowledge:

(1)The Report complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; as amended, and

(2)The consolidated 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:   February 19, 2013

/s/ Constance H. Lau

Constance H. Lau

President and Chief Executive Officer

/s/ James A. Ajello

James A. Ajello

Executive Vice President,

Chief Financial Officer and Treasurer

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.