Exhibit 99.1

InfraREIT, Inc. 1807 Ross Avenue, 4th Floor Dallas, TX 75201

PRESS RELEASE

InfraREIT Comments on SEC Filing by Related Party

DALLAS, TEXAS, May 4, 2016—InfraREIT, Inc. (NYSE: HIFR) (InfraREIT or the Company) today announced that its shareholder Hunt Consolidated Inc. (“Hunt”) filed an amendment to Hunt’s Schedule 13D with the U.S. Securities and Exchange Commission disclosing, among other things, the following:

Hunt had previously disclosed its intent to commence business combination-related discussions with the Company in Hunt’s Schedule 13D amendment dated June 8, 2015. The Conflicts Committee of InfraREIT’s board of directors has informed the Company that it intends to carefully consider any potential transactions involving Oncor and the Company, if and when Hunt elects to continue discussions and a proposal, if any, is made to the Conflicts Committee. InfraREIT has not received a proposal regarding any potential combination and does not intend to comment further on today’s filing by Hunt.

About InfraREIT, Inc.

InfraREIT is a real estate investment trust that owns rate-regulated electric transmission and distribution assets in the state of Texas. The Company is externally managed by Hunt Utility Services, LLC, an affiliate of Hunt Consolidated, Inc. (a diversified holding company based in Dallas, Texas and managed by the Ray L. Hunt family) and the Company’s shares are traded on the New York Stock Exchange under the symbol “HIFR”. Additional information on InfraREIT is available at http://www.InfraREITInc.com.

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Forward-Looking Statements

This press release contains “forward-looking statements” within the meaning of the federal securities laws. These statements state the current expectations or intentions of the Company regarding future events, which by their nature, involve known and unknown risks and uncertainties. Factors that could cause actual results to differ materially from those contemplated above include, among others, the following: (a) a determination by Hunt or potential equity investors not to engage in or continue discussions or to make any proposal with respect to a transaction with the Company, (b) a definitive agreement regarding an acquisition of Oncor with a third party other than Hunt, (c) events or developments that would prevent or restrict acquisition of Oncor within a certain timeframe, or at all, including the risk that required regulatory approvals would not be obtained, or obtained on terms that Hunt or its potential investors deem unacceptable, and (d) events or developments that would prevent or restrict the Company from successfully negotiating the nature of or terms applicable to a possible transaction involving Oncor and the Company.

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Any forward-looking statement made by the Company in this press release is based only on information currently available to InfraREIT and speaks only as of the date on which it is made. InfraREIT undertakes no obligation to update or revise any forward-looking statements, whether as a result of new information, future events or otherwise, other than required by applicable law.

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