Exhibit 99.1

PRESS RELEASE

InfraREIT Announces First Quarter 2015 Results

DALLAS, TEXAS, May 13, 2015—InfraREIT, Inc. (NYSE: HIFR) (“InfraREIT” or the “Company”) today reported financial results for the three months ending March 31, 2015, and the Company’s financial outlook.

InfraREIT reported the following first quarter 2015 financial highlights:

“Our financial performance during the quarter reflected the solid growth in our core business,” said David A. Campbell, Chief Executive Officer of InfraREIT. “Our forward outlook and ongoing growth prospects remain strong, enhanced by the combination of our REIT structure, pipeline of opportunities, and alignment with the Hunt organization.”

Successfully Closed Initial Public Offering

On January 29, 2015, InfraREIT priced its initial public offering of 23 million shares of common stock, including the over-allotment, for gross proceeds of $529 million before fees and expenses. InfraREIT shares began trading on January 30, 2015, under the symbol HIFR on the New York Stock Exchange. The IPO closed on February 4, 2015.

InfraREIT, L.L.C. merged with and into InfraREIT, Inc. (Merger) immediately after the closing of the IPO. InfraREIT, Inc. is the surviving entity and general partner of InfraREIT Partners, LP (Operating Partnership). The Company used approximately $223 million of the net proceeds from the offering to repay outstanding indebtedness. The Company used an additional $172 million of the net proceeds from the IPO to fund the cash portion of the consideration issued in the Merger and retained the remaining net proceeds for general corporate purposes.

Higher Lease Revenue Led to Strong First Quarter 2015 Results

Lease revenue of $29.4 million for the three months ended March 31, 2015, increased $4.6 million, or approximately 19 percent, compared to the same period in 2014. Base rent contributed $29.4 million for the first quarter of 2015, compared to $24.8 million for the first quarter of 2014. The increase in base rent was driven by the addition of assets under lease during the year ended December 31, 2014. There was no percentage rent recognized during the three months ended March 31, 2015 or 2014, as an annual specified breakpoint must be met under the Company’s leases before InfraREIT recognizes any percentage rent. InfraREIT expects to recognize little to no percentage rent during the first or second quarters of each year and expects to recognize the largest amounts during the third and fourth quarters of each year.

General and administrative expenses were $48.7 million in the first quarter of 2015, compared to $3.4 million for the first quarter of 2014. Higher general and administrative expense resulted from the issuance of 1.7 million shares of common stock to Hunt-InfraREIT, L.L.C. (Hunt-InfraREIT) as a non-cash reorganization advisory fee, resulting in an expense of $44.9 million in the first quarter of 2015. Depreciation expense was $9.5 million and $8.5 million for the first quarter of 2015 and 2014, respectively. The increase in depreciation expense was due to the additional assets placed in service during 2014.

Net interest expense was $7.4 million and $7.7 million during the first quarter of 2015 and 2014, respectively. The quarter-over-quarter decrease resulted from lower interest expense related to the repayment of the outstanding amounts under InfraREIT’s revolving credit facilities in February 2015.

Other income, net was $0.6 million during the first quarter of 2015 compared to other expense, net of $0.1 million for the three months ended March 31, 2014. The increase in other income (expense), net was due to a change in fair value of the Operating Partnership’s contingent consideration owed to Hunt-InfraREIT during the three months ended March 31, 2014. There was no such expense during the same period of the current year.

The net loss was $35.9 million in the first quarter of 2015, or $(0.65) per diluted share, including the effect of a $44.9 million non-cash expense incurred in connection with the IPO. Net income for the first quarter of 2014 was $5.0 million, or $0.11 per diluted share.

Cash available for distribution before noncontrolling interest (CAD) was $18.3 million, or $0.30 CAD per share, in the first quarter of 2015, compared to $12.7 million, or $0.28 CAD per share in the same period in 2014. CAD per share for the first quarter of 2015 was based on 60.6 million shares outstanding as of March 31, 2015, compared to 45.5 million shares outstanding as of March 31, 2014.

On an adjusted basis, earnings before noncontrolling interest and before interest, taxes, depreciation and amortization (Adjusted EBITDA) was $34.4 million in the first quarter of 2015, an increase of 22 percent, compared to $28.2 million in the same period in 2014. Funds from Operations before noncontrolling interest (FFO) was $(26.4) million for the first quarter of 2015 compared to $13.5 million from the same period in 2014. FFO on an adjusted basis (AFFO) was $26.8 million for the first quarter of 2015, an increase of 32 percent, compared to $20.3 million in the same period in 2014.

The Company uses many metrics “before noncontrolling interest” as InfraREIT feels it is important to evaluate the complete business, including the portion attributable to the minority ownership of the Operating Partnership. Inclusion of the phrase “before noncontrolling interest” to modify CAD, EBITDA, FFO and AFFO means the Company’s calculation of that metric before any reduction as a result of the noncontrolling interest in the Operating Partnership.

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Liquidity and Capital Resources

As of March 31, 2015, the Company had $86.5 million of unrestricted cash and cash equivalents. The Company primarily utilizes its cash for the payment of capital expenditures, operating expenses, debt service and dividend payments. InfraREIT also had $1.7 million of restricted cash and $325.0 million of unused capacity under its revolving credit facilities as of March 31, 2015.

Asset Sales

In October 2014, InfraREIT, L.L.C.’s board of directors approved a plan to sell its assets related to the Cross Valley transmission line (Cross Valley) and Golden Spread Electric Coop (GSEC) interconnection to Hunt Consolidated, Inc. and its subsidiaries (Hunt) and certain InfraREIT pre-IPO investors. Effective January 15, 2015, the Company sold all of the assets related to Cross Valley to Hunt and the pre-IPO investors and the assets related to GSEC to Hunt. Both Cross Valley and GSEC are designated as “ROFO Projects” under the Company’s development agreement with Hunt. ROFO Projects are identified projects that are being developed by Hunt with respect to which InfraREIT has a right of first offer under the development agreement. In exchange for the sale of the Cross Valley and GSEC assets, the Company received $41.2 million in cash which equaled the construction work in progress (CWIP) of the projects on the date of sale plus reimbursement of out of pocket expenses associated with the Cross Valley project financing.

Outlook and Guidance Update

InfraREIT is reaffirming its previously provided guidance. CAD per share for the full year of 2015 is estimated at $1.07 per share. The Company anticipates capital expenditures in the range of $745 million to $775 million for the period of 2015 through 2017. InfraREIT anticipates that it will be able to fund its estimated Footprint Projects’ capital expenditures through the end of 2017 without raising proceeds from additional equity offerings. Footprint Projects are projects that expand the Company’s transmission and distribution assets which are currently in InfraREIT’s geographic footprint.

The Company also expects the three-year cumulative annual growth rate of its CAD per share to be in the range of 10 percent to 15 percent through December 31, 2018. The Company expects to achieve the lower half of this growth range solely through Footprint Projects, and to exceed the midpoint of the range through the acquisition of Cross Valley and GSEC from Hunt. The Company believes it could achieve the top of the range through additional Footprint Projects or acquisitions. Regarding InfraREIT’s consolidated debt profile, the Company targets debt as a percentage of total capitalization at or below 60 percent and AFFO to debt of at least 12 percent.

The guidance provided above represents forward-looking statements, which are based on current economic conditions and estimates, and the Company does not include other potential impacts, such as changes in accounting or unusual items. Supplemental information relating to the Company’s financial outlook is posted in the Investor Relations section of the Company’s Web site at www.InfraREITInc.com.

Monthly ROFO Project Updates

InfraREIT expects to provide monthly “ROFO Project Updates” on or about the 15^th day of the month beginning June 2015. These ROFO Project Updates will be found on the Company’s Web site (www.InfraREITInc.com) under the “Hunt Transmission-Our Developer” and “Investor Relations” sections.

Dividends and Distributions

On March 6, 2015, InfraREIT’s Board of Directors declared a cash distribution by the Operating Partnership to all unit holders of record, including InfraREIT, Inc., on March 31, 2015 of $0.14 per unit for a total distribution of $8.5 million, $6.1 million of which was allocated to InfraREIT, Inc. Also, on March 6, 2015, the Company’s board of directors declared a cash dividend to shareholders of record on March 31, 2015, of $0.14 per share for a total of $6.1 million. The $0.14 per share of common stock was calculated from the closing date of its IPO on February 4, 2015, through March 31, 2015. The cash distribution and cash dividend were paid on April 23, 2015.

On January 13, 2015, InfraREIT, L.L.C.’s board of directors declared a pre-IPO cash distribution by the Operating Partnership to all unit holders of $0.26 per unit, for a total distribution of $11.7 million, and a cash dividend to shareholders of $0.26 per share, for a total of $9.0 million, for record holders on January 20, 2015. The cash distribution and cash dividend were both paid on January 29, 2015.

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Conference Call and Webcast

As previously announced, management will host a teleconference call May 13, 2015, at 10 a.m. U.S. Central

(11 a.m. U.S. Eastern). David A. Campbell, Chief Executive Officer, and Brant Meleski, Chief Financial Officer, will discuss InfraREIT’s first quarter results and financial outlook.

Investors and analysts are invited to participate in the call by phone at 1-877-870-4263 (access code: 10063016) or via the Internet at www.InfraREITInc.com. A replay of the call will be available on the Company Web site or by phone at 1-877-344-7529 (access code: 10063016) for a seven-day period following the call.

Non-GAAP Measures

This press release contains certain financial measures that are not recognized under generally accepted accounting principles (GAAP). These non-GAAP measures are presented because InfraREIT’s management believes they help investors understand InfraREIT’s business, performance and ability to earn and distribute cash to its stockholders by providing perspectives not immediately apparent from net income. These measures are also measures frequently used by securities analysts, investors and other interested parties. The presentation of CAD, EBITDA, Adjusted EBITDA, FFO and AFFO in this press release are not intended to be considered in isolation or as a substitute for, or superior to, the financial information prepared and presented in accordance with GAAP. In addition, InfraREIT’s method of calculating these measures may be different from methods used by other companies, and, accordingly, may not be comparable to similar measures as calculated by other companies that do not use the same methodology as InfraREIT. Reconciliations of these measures to their most directly comparable GAAP measures are included in the Schedules to this press release.

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). The Company’s shares are traded on the New York Stock Exchange under the symbol “HIFR.” Additional information on InfraREIT, Inc. is available at www.InfraREITInc.com.

Forward-Looking Statements

This press release contains forward-looking statements within the meaning of the federal securities laws. These statements give InfraREIT management’s current expectations, contain projections of results of operations or financial condition or forecasts of future events. Words such as “could,” “will,” “may,” “assume,” “forecast,” “strategy,” “guidance,” “outlook,” “target,” “expect,” “intend,” “plan,” “estimate,” “anticipate,” “believe,” or “project” and similar expressions are used to identify forward-looking statements. Without limiting the generality of the foregoing, forward-looking statements contained in this press release include InfraREIT’s expectations regarding its anticipated financial and operational performance, including projected or forecasted financial results, project timing, distributions to stockholders, dividend growth, capital expenditures, lease payments, CAD growth, AFFO-to-debt ratios and capitalization matters. Forward-looking statements can be affected by assumptions used or known or unknown risks or uncertainties. Consequently, no forward-looking statements can be guaranteed and actual results may differ materially and adversely from those reflected in the forward-looking statements. Factors that could cause actual results to differ materially from those indicated in the forward-looking statements include, among others, the following: (a) risks that the capital expenditures the Company expects will not materialize for a variety of reasons, including as a result of more significant reductions, relative to current expectations, in oil and gas drilling and related midstream and service company activities in the Permian Basin due to lower oil and gas prices, (b) the Company’s ability to acquire ROFO Projects from Hunt, (c) the Company’s current reliance on its tenant for all of its revenues and, as a result, its dependency on the tenant’s solvency and financial and operating performance, (d) defaults on or non-renewal or early termination of leases by the Company’s tenant, (e) changes in the regulated rates the tenants of the Company’s assets may charge their customers and (f) defaults on or non-renewal or early termination of leases by the Company’s tenant. These and other applicable uncertainties, factors and risks are described more fully in the Company’s filings with the Securities and Exchange Commission.

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.

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InfraREIT, Inc.

CONSOLIDATED STATEMENTS OF INCOME

(In thousands, except share amounts)

(Unaudited)

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InfraREIT, Inc.

CONSOLIDATED BALANCE SHEETS

(In thousands, except share amounts)

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InfraREIT, Inc.

CONSOLIDATED STATEMENTS OF CASH FLOWS

(In thousands)

(Unaudited)

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Non-GAAP Measures

Schedule 1

InfraREIT, Inc.

Explanation and Reconciliation of CAD

CAD

The Company’s definition of CAD includes a deduction of the portion of capital expenditures needed to maintain its net assets. This amount is equal to the depreciation expense within the applicable period. The portion of the capital expenditures in excess of depreciation, which the Company refers to as growth capital expenditures, will increase its net assets. CAD also includes various other adjustments from net income, as outlined below and described in more detail on Schedule 2 and 3.

The following sets forth a reconciliation of net income (loss) attributable to InfraREIT to CAD:

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Schedule 2

InfraREIT, Inc.

Explanation and Reconciliation of EBITDA and Adjusted EBITDA

EBITDA and Adjusted EBITDA

InfraREIT defines EBITDA as net income (loss) before any reduction as a result of net income (loss) attributable to noncontrolling interest and before interest expense, net; income tax expense; depreciation and amortization. Adjusted EBITDA is defined as EBITDA adjusted in a manner the Company believes is appropriate to show its core operational performance, including: (a) non-cash reorganization structuring fee, (b) effect of percentage rent, (c) effect of straight-line rent, (d) reorganization expenses and (e) other income (expense), net.

The following table sets forth a reconciliation of net income (loss) attributable to InfraREIT to EBITDA and Adjusted EBITDA:

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Schedule 3

InfraREIT, Inc.

Explanation and Reconciliation of FFO and AFFO

FFO and AFFO

The National Association of Real Estate Investment Trusts (NAREIT) defines FFO as net income (computed in accordance with GAAP), excluding gains and losses from sales of property (net) and impairments of depreciated real estate, plus real estate depreciation and amortization (excluding amortization of deferred financing costs) and after adjustments for unconsolidated partnerships and joint ventures. Applying the NAREIT definition to the Company’s consolidated financial statements, which is the basis for the FFO presented in the press release and the reconciliation below, results in FFO representing net (loss) income before any reduction as a result of net (loss) income attributable to noncontrolling interest, depreciation, impairment of assets and gain (loss) on sale of assets. FFO does not represent cash generated from operations as defined by GAAP and it is not indicative of cash available to fund all cash needs, including distributions.

AFFO is defined as FFO adjusted in a manner the Company believes is appropriate to show its core operational performance, including: (a) non-cash reorganization structuring fee, (b) effect of percentage rent, (c) effect of straight-line rent, (d) reorganization expenses, and (e) other income (expense), net.

The following table sets forth a reconciliation of net income (loss) attributable to InfraREIT to FFO and AFFO:

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For additional information, contact:

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