Exhibit 99.1

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE

919 CONGRESS AVENUE / (512) 236-6599 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST ANNOUNCES THERE WILL BE NO FIRST QUARTER 2015 DISTRIBUTION

AUSTIN, TEXAS April 6, 2015—TEL OFFSHORE TRUST (the “Trust”) announced that there will be no trust distribution for the first quarter of 2015 for unitholders of record on March 31, 2015. The Trust has not been able to make a distribution to unitholders for twenty-five consecutive quarters, or since January 9, 2009.  The financial and operating information included herein for the Trust’s first quarter of 2015 reflects financial and operating information with respect to the royalty properties for the months of November and December 2014 and January 2015.

Gross proceeds for the burdened royalty properties exceeded development and production costs for the months of November and December 2014 and January 2015 by $1,947,303, or $486,826 net to the entire overriding royalty interest, and $292,096 attributable to the Trust.  The excess proceeds, net to the entire overriding royalty interest, were applied to reduce the accumulated excess cost carryforward, which represents the amount by which the aggregate development and production costs for the burdened royalty properties since November 2008 have exceeded the related proceeds of the production.

Gas revenues recorded by Chevron USA, Inc. (“Chevron”), the Managing General Partner of the TEL Offshore Trust Partnership (the “Partnership”) for the quarter on the burdened royalty properties increased approximately 97% to $318,440 from $161,582 in the fourth quarter of 2014. Natural gas volumes during the first quarter of 2015 increased approximately 80% to 79,063 Mcf from 43,897 Mcf during the fourth quarter of 2014. The increase in production is primarily due to production fluctuations within the normal operating range. Excluding the impact of prior period adjustments, the average price received for natural gas production increased approximately 7% to $3.95 per Mcf in the first quarter of 2015 from $3.68 per Mcf in the fourth quarter of 2014. Gas products revenues during the first quarter of 2015 decreased approximately 63% from $80,314 in the fourth quarter of 2014 to $29,768 in the first quarter of 2015.

Crude oil and condensate revenues recorded by Chevron for the quarter on the burdened royalty properties decreased approximately 39% to $2,616,204 in the first quarter of 2015 from $4,303,555 in the fourth quarter of 2014. Crude oil and condensate volumes during the first quarter of 2015 decreased approximately 21% to 34,539 barrels, compared to 43,936 barrels during the fourth quarter of 2014. The decrease in production is primarily due to production fluctuations within the normal operating range. Excluding the impact of prior period adjustments, the average price received for crude oil and condensate production decreased approximately 21% to $77.64 per barrel in the first quarter of 2015 from $97.95 per barrel in the fourth quarter of 2014.  The production period for the first quarter of 2015 includes November and December 2014 and January 2015. Although the average price received for crude oil and condensate decreased from the prior quarter, the decrease does not fully reflect the significant recent declines in the price of crude oil and it is anticipated that the average price received for the foreseeable future may be further reduced in light of the current reduced price environment for crude oil and natural gas.

Capital expenditures were $172 in the first quarter of 2015 as compared to $(44) in the fourth quarter of 2014. Operating expenses decreased by approximately 21%, or $239,162 to $900,970 in the first quarter of 2015 from $1,140,132 in the fourth quarter of 2014.

As discussed above, gross proceeds for the royalty properties for the first quarter of 2015 exceeded development and production costs thereof, with the portion of such excess attributable to the Trust’s interest in the remaining 15% royalty interest equal to approximately $292,096.  As of January 31, 2015, after applying the net proceeds for the months of November and December 2014 and January 2015, the amount by which the aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties has been reduced to approximately $2.3 million, net to the entire royalty (or approximately $1.4 million, net to the Trust’s interest in the remaining 15% royalty interest) as compared to approximately $2.8 million (or approximately $1.7 million, net to the Trust’s interest in the remaining 15% royalty interest) as of October 31, 2014. The Trust will not receive any distribution of net proceeds until such time as the proceeds of production exceed the accumulated excess cost carryforward. As a result, the Trust will not be receiving any net proceeds for the first quarter of 2015.  In light of the continuing expenses of the Trust and the lack of any distributions and any assurances as to the actual timing of any future distributions, the Trustees initiated the previously disclosed probate proceeding in the Probate Court of Travis County, Texas (the “Probate Proceeding”) and continue to evaluate all alternatives available to the Trust to obtain funds or to reduce the ongoing costs and expenses of the Trust. As a result, there is no guarantee that any further distributions form the Trust will be made.

With respect to the Probate Proceeding, the Trust is continuing the process of serving the Petition for Modification and Termination of the Trust (the “Petition”) on the Trust’s unitholders and it is expected that service will be completed in the second quarter of 2015.  The Trustees will then request the court to appoint an ad litem to represent any unitholders that have not been personally served. It is anticipated that the trial will be during the fourth quarter of 2015, assuming there are no unexpected delays.  The Trust and the Trustees wish to confirm that they are not seeking a finding of any liability against any of the Trust’s unitholders in the Probate Proceeding and that they are not seeking any money or damages from any of the Trust’s unitholders.  Under Texas law, the beneficiaries of the Trust are necessary parties to the Probate Proceeding and, therefore, the Trustees are required to serve the Petition on the Trust’s unitholders.  It is not the purpose of the Probate Proceeding to seek any recovery from the Trust’s unitholders, and the Trustees will not seek a judgment against the Trust’s unitholders.  The Trust will continue to provide information regarding the status of the Probate Proceeding in its filings with the Securities and Exchange Commission (“SEC”) and, to the extent appropriate, will issue press releases providing additional information regarding the Probate Proceeding.  All documents that are filed in the Probate Proceeding and all of the Trust’s future filings with the SEC during the Probate Proceedings can be viewed at: www.andrewskurth.com/teloffshoretrust.

This press release contains forward-looking statements.  Although the Managing General Partner of the TEL Offshore Trust Partnership has advised the Trust that the Managing General Partner believes that the expectations contained in this press release are reasonable, no assurances can be given that such expectations will prove to be correct. The Working Interest Owners alone control historical operating data, and handle receipt and payment of funds relating to the royalty properties and payments to the Trust for the related royalty. The Trustees of the Trust cannot assure that errors or adjustments by the Working Interest Owners, whether historical or future, will not affect future royalty income and distributions by the Trust.  Other important factors that could cause these statements to differ materially include the pending Probate Proceeding and the possibility that the Trust way be terminated, the Trust’s utilization of its cash reserves to pay expenses and the lack of net proceeds received by the Trust, delays and costs in connection with repairs or replacements of hurricane-damaged facilities and pipelines, including

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third-party transportation systems, the actual results of drilling operations, risks inherent in drilling and production of oil and gas properties, the Trust’s ability to pay its liabilities, and other factors described in the Trust’s Form 10-K for the year ended December 31, 2014 under “Item 1A. Risk Factors,” as well as other risks identified from time to time in its reports on Form 10-Q and Form 8-K as filed with the Securities and Exchange Commission.  Statements made in this press release are qualified by the cautionary statements made in these risk factors. The Trust does not intend, and assumes no obligations, to update any of the statements included in this press release.

The Bank of New York Mellon Trust Company, N.A.

AS CORPORATE TRUSTEE

CONTACT:  Michael J. Ulrich

(512) 236-6599

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