Exhibit 4.4

CenterPoint Energy Houston Electric, LLC

1111 Louisiana

Houston, TX 77002

CENTERPOINT ENERGY HOUSTON ELECTRIC, LLC

TO

THE BANK OF NEW YORK MELLON TRUST COMPANY, NATIONAL ASSOCIATION

(successor in trust to JPMORGAN CHASE BANK),

as Trustee

TWENTY-FOURTH SUPPLEMENTAL INDENTURE

Dated as of May 18, 2016

Supplementing the General Mortgage Indenture

Dated as of October 10, 2002

Filed under file number 030004510538 in the

Office of the Secretary of State as an instrument

granting a security interest by a public utility

THIS INSTRUMENT GRANTS A SECURITY INTEREST BY A UTILITY

THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS

This instrument is being filed pursuant to Chapter 261 of the Texas Business and Commerce Code

TWENTY-FOURTH SUPPLEMENTAL INDENTURE, dated as of May 18, 2016, between CENTERPOINT ENERGY HOUSTON ELECTRIC, LLC, a limited liability company organized and existing under the laws of the State of Texas (herein called the “Company”), having its principal office at 1111 Louisiana, Houston, Texas 77002, and THE BANK OF NEW YORK MELLON TRUST COMPANY, NATIONAL ASSOCIATION (successor in trust to JPMORGAN CHASE BANK), a limited purpose national banking association duly organized and existing under the laws of the United States, as Trustee (herein called the “Trustee”), the office of the Trustee at which on the date hereof its corporate trust business is administered being 601 Travis Street, 16th Floor, Houston, Texas 77002.

RECITALS OF THE COMPANY

WHEREAS, the Company has heretofore executed and delivered to the Trustee a General Mortgage Indenture dated as of October 10, 2002, as supplemented and amended (the “Indenture”), providing for the issuance by the Company from time to time of its bonds, notes or other evidence of indebtedness to be issued in one or more series (in the Indenture and herein called the “Securities”) and to provide security for the payment of the principal of and premium, if any, and interest, if any, on the Securities; and

WHEREAS, the Company, in the exercise of the power and authority conferred upon and reserved to it under the provisions of the Indenture and pursuant to appropriate resolutions of the Manager, has duly determined to make, execute and deliver to the Trustee this Twenty-Fourth Supplemental Indenture to the Indenture as permitted by Sections 201, 301, 403(2) and 1401 of the Indenture in order to establish the form or terms of, and to provide for the creation and issuance of, a twenty-fifth series of Securities under the Indenture in an initial aggregate principal amount of $300,000,000 (such twenty-fifth series being hereinafter referred to as the “Twenty-Fifth Series”); and

WHEREAS, all things necessary to make the Securities of the Twenty-Fifth Series, when executed by the Company and authenticated and delivered by the Trustee or any Authenticating Agent and issued upon the terms and subject to the conditions hereinafter and in the Indenture set forth against payment therefor the valid, binding and legal obligations of the Company and to make this Twenty-Fourth Supplemental Indenture a valid, binding and legal agreement of the Company, have been done;

NOW, THEREFORE, THIS TWENTY-FOURTH SUPPLEMENTAL INDENTURE WITNESSETH that, in order to establish the terms of a series of Securities, and for and in consideration of the premises and of the covenants contained in the Indenture and in this Twenty-Fourth Supplemental Indenture and for other good and valuable consideration the receipt and sufficiency of which are hereby acknowledged, it is mutually covenanted and agreed as follows:

ARTICLE ONE

DEFINITIONS AND OTHER PROVISIONS

OF GENERAL APPLICATION

Section 101. Definitions. Each capitalized term that is used herein and is defined in the Indenture shall have the meaning specified in the Indenture unless such term is otherwise defined herein.

ARTICLE TWO

TITLE, FORM AND TERMS OF THE BONDS

Section 201. Title of the Bonds. This Twenty-Fourth Supplemental Indenture hereby creates a series of Securities designated as the “1.85% General Mortgage Bonds, Series Y, due 2021” (the “Series Y Bonds”). For purposes of the Indenture, the Series Y Bonds shall constitute a single series of Securities and, subject to the provisions, including, but not limited to Article Four of the Indenture, the Series Y Bonds shall be issued in an aggregate principal amount of $300,000,000.

Section 202. Form and Terms of the Bonds. The form and terms of the Series Y Bonds will be set forth in an Officer’s Certificate delivered by the Company to the Trustee pursuant to the authority granted by this Twenty-Fourth Supplemental Indenture in accordance with Sections 201 and 301 of the Indenture.

Section 203. Treatment of Proceeds of Title Insurance Policy. Any moneys received by the Trustee as proceeds of any title insurance policy on Mortgaged Property of the Company shall be subject to and treated in accordance with the provisions of Section 607(2) of the Indenture (other than the last paragraph thereof).

ARTICLE THREE

MISCELLANEOUS PROVISIONS

The Trustee makes no undertaking or representations in respect of, and shall not be responsible in any manner whatsoever for and in respect of, the validity or sufficiency of this Twenty-Fourth Supplemental Indenture or the proper authorization or the due execution hereof by the Company or for or in respect of the recitals and statements contained herein, all of which recitals and statements are made solely by the Company.

Except as expressly amended and supplemented hereby, the Indenture shall continue in full force and effect in accordance with the provisions thereof and the Indenture is in all respects hereby ratified and confirmed. This Twenty-Fourth Supplemental Indenture and all of its provisions shall be deemed a part of the Indenture in the manner and to the extent herein and therein provided.

This Twenty-Fourth Supplemental Indenture shall be governed by, and construed in accordance with, the law of the State of New York.

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This Twenty-Fourth Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument.

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IN WITNESS WHEREOF, the parties hereto have caused this Twenty-Fourth Supplemental Indenture to be duly executed as of the day and year set forth below and effective as of the day and year first above written.

ACKNOWLEDGMENT

On the     day of         , 2016, before me personally came Kristie L. Colvin, to me known, who, being by me duly sworn, did depose and say that she resides in         , Texas; that she is the Senior Vice President and Chief Accounting Officer of CenterPoint Energy Houston Electric, LLC, a Texas limited liability company, the limited liability company described in and which executed the foregoing instrument; and that she signed her name thereto by authority of the sole manager of said limited liability company.

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ACKNOWLEDGMENT

State of California

County of         )

personally appeared                             , who proved to me on the basis of satisfactory evidence to be the person(s) whose name(s) is/are subscribed to the within instrument and acknowledged to me that he/she/they executed the same in his/her/their authorized capacity(ies), and that by his/her/their signature(s) on the instrument the person(s), or the entity upon behalf of which the person(s) acted, executed the instrument.

I certify under PENALTY OF PERJURY under the laws of the State of California that the foregoing paragraph is true and correct.

WITNESS my hand and official seal.

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