Exhibit 99.1

Acer Therapeutics Plans Clinical Trial for EDSIVO™ (celiprolol) Following Type B FDA Meeting

Phase 3, randomized, double-blind, placebo-controlled, decentralized clinical trial estimated to take approximately 3.5 years to complete once fully enrolled

FDA indicates agreement with submission of proposed protocol under a Special Protocol Assessment (SPA) with possible breakthrough designation

NEWTON, MA – June 10, 2021 – Acer Therapeutics Inc. (Nasdaq: ACER), a pharmaceutical company focused on the acquisition, development and commercialization of therapies for serious rare and life-threatening diseases with significant unmet medical needs, today announced that following a recent Type B meeting with the U.S. Food and Drug Administration (FDA) regarding Acer’s proposed EDSIVO™ (celiprolol) development plan, the company is now planning a pivotal clinical trial in patients with COL3A1+ vascular Ehlers-Danlos Syndrome (vEDS).

In the Type B meeting, Acer discussed conducting a U.S.-based prospective, randomized, double-blind, placebo-controlled, decentralized clinical trial in patients with COL3A1+ vEDS, and sought the Agency’s opinion on various proposed design features of the study. The official meeting minutes Acer recently received from the FDA confirm details of that discussion, including: the acceptability of a decentralized (virtual) clinical trial design and use of an independent centralized adjudication committee; acceptability of a primary endpoint based on clinical events associated with disease outcome; agreement with modest safety data collection (based on the known safety profile of the drug^1,2,3,4) and no pharmacokinetic (PK) data needing to be collected; and a statistical plan that considers the rare disease classification of vEDS.

In the second half of 2021, Acer intends to submit a protocol for the prospective study, along with an investigational new drug application (IND), request breakthrough therapy designation, and coordinate with FDA to reach agreement on a Special Protocol Assessment (SPA). Based on initial power calculations, Acer anticipates that the trial should enroll approximately 200 COL3A1+ vEDS patients in the U.S., and the duration of the clinical trial is estimated to be approximately 3.5 years to complete once fully enrolled.

“We appreciate the guidance and flexibility provided by FDA on the design of this proposed clinical trial,” said Chris Schelling, CEO and Founder of Acer. “This trial, along with the results from the prior BBEST trial¹, should answer whether EDSIVO™ demonstrates substantial evidence of effectiveness by reducing vEDS-related events. Over the next six months, we intend to work closely with FDA to finalize the protocol for the pivotal trial, collaborate with vEDS advocacy groups to identify COL3A1+ patients who may be interested in participating in the trial in order to expedite enrollment, and achieve first patient dosed as quickly as possible. Our progress to date on the EDSIVO™ program is the direct result of our unwavering and ongoing commitment to patients with rare diseases. We look forward to continuing its development for treatment of vEDS patients who desperately need a therapy.”

For more information on the trial as it becomes available, please visit: www.discoverceliprolol.com.

The conduct and completion of the EDSIVO™ pivotal clinical trial is subject to Acer’s ability to obtain up to approximately $10 million of funding. Such funding may come from one or more of a number of current and future sources, including but not limited to current cash, a strategic partnership, other non-dilutive sources and potential ACER-001 revenue. Acer believes its cash and cash equivalents available as of March 31, 2021, plus up to $20.0 million of Development Payments per the ACER-001 Collaboration Agreement with Relief Therapeutics, are sufficient to fund its currently anticipated operating and capital requirements into mid-2022, excluding support for planned EDSIVO™ and osanetant clinical trials.

EDSIVO™ is an investigational drug and is not currently FDA approved for any indication. There can be no assurance that the funding to conduct and complete the clinical trial will be obtained, that the clinical trial will be successful, or that the resubmission of the original New Drug Application will be approved.

About Breakthrough Therapy Designation

The FDA’s breakthrough therapy designation is intended to expedite the development and review of new treatments for serious or life-threatening conditions. The designation entitles the company developing a therapy to more intensive FDA guidance on an efficient and accelerated development program, as well as eligibility for other actions to expedite FDA review, such as rolling submission and priority review. To earn breakthrough designation, a treatment must show encouraging early clinical results demonstrating substantial improvement over available therapies with regard to a clinically significant endpoint, or it must fulfill an unmet need.

About vEDS

Ehlers-Danlos syndrome (EDS) is an inherited disorder caused by mutations in the genes responsible for the structure, production, or processing of collagen, an important component of the connective tissues in the human body, or proteins that interact with collagen. EDS is a spectrum disorder where patients present with various forms, the most serious of which is vEDS, also known as EDS type IV, which is generally caused by a mutation in the COL3A1 gene. vEDS causes abnormal fragility in blood vessels, which can give rise to aneurysms, abnormal connections between blood vessels known as arteriovenous fistulas, arterial dissections, and spontaneous vascular ruptures, all of which can be potentially life-threatening. Gastrointestinal and uterine fragility or rupture also commonly occur in vEDS patients. Spontaneous arterial rupture has a peak incidence in the third or fourth decade of life in vEDS patients but may occur earlier and is the most common cause of sudden death in vEDS patients. Arterial rupture or dissection events occur in about 25% of patients before the age of 20 but increase to roughly 90% of patients by the age of 40. The median survival age of vEDS patients in the U.S. is 51 years, with arterial rupture being the most common cause of sudden death.⁵

About EDSIVO™ (celiprolol)

Acer is developing EDSIVO™, a new chemical entity (NCE), for the treatment of COL3A1+ vEDS patients. Acer’s EDSIVO™ NDA was originally submitted based on data obtained from the BBEST trial¹ and accepted for filing in October 2018 with priority review. Following FDA review, Acer received a Complete Response Letter (CRL) stating that it will be necessary to conduct an adequate and well-

controlled trial to determine whether celiprolol reduces the risk of clinical events in patients with vEDS. Acer subsequently appealed the FDA decision. While FDA denied the appeal, it described possible paths forward for Acer to explore. Following its Type B meeting with FDA in the second quarter of 2021, Acer has decided to conduct a clinical trial for EDSIVO™. There can be no assurance that the resulting data from the trial would be adequate to support approval of an NDA, although having a SPA agreement in place would indicate concurrence by FDA with the adequacy and acceptability of specific critical elements of overall protocol design (e.g., conduct, entry criteria, dose selection, endpoints, and planned analyses) for a study intended to support a future marketing application.

About Acer Therapeutics Inc.

Acer is a pharmaceutical company focused on the acquisition, development and commercialization of therapies for serious rare and life-threatening diseases with significant unmet medical needs. Acer’s pipeline includes four programs: ACER-001 (sodium phenylbutyrate) for the treatment of various inborn errors of metabolism, including urea cycle disorders (UCDs) and Maple Syrup Urine Disease (MSUD); EDSIVO™ (celiprolol) for the treatment of vascular Ehlers-Danlos syndrome (vEDS) in patients with a confirmed type III collagen (COL3A1) mutation; ACER-801 (osanetant) for the treatment of induced Vasomotor Symptoms (iVMS); and ACER-2820 (emetine), a host-directed therapy against a variety of infectious diseases, including COVID-19. Each of Acer’s product candidates is believed to present a comparatively de-risked profile, having one or more of a favorable safety profile, clinical proof-of-concept data, mechanistic differentiation and/or accelerated paths for development through specific programs and procedures established by the FDA. In March 2021, Acer entered into a Collaboration and License Agreement with Relief Therapeutics for development and commercialization of ACER-001. For more information, visit www.acertx.com.

References

Forward-Looking Statements

This press release contains “forward-looking statements” that involve substantial risks and uncertainties for purposes of the safe harbor provided by the Private Securities Litigation Reform Act of 1995. All statements, other than statements of historical facts, included in this press release regarding strategy, future operations, timelines for clinical study enrollment or regulatory actions, or otherwise, future financial position, future revenues, projected expenses, regulatory submissions, actions or approvals, cash position, liquidity, prospects, plans and objectives of management are forward-looking statements. Examples of such statements include, but are not limited to, statements relating to the potential for our product candidates to safely and effectively treat diseases and to be approved for

marketing; the commercial or market opportunity of any of our product candidates in any target indication and any territory; our ability to secure the additional capital necessary to fund our various product candidate development programs; the adequacy of our capital to support our future operations and our ability to successfully fund, initiate and complete clinical trials and regulatory submissions for EDSIVO™ or our other products; the ability to protect our intellectual property rights; our strategy and business focus; and the development, expected timeline and commercial potential of any of our product candidates. We may not actually achieve the plans, carry out the intentions or meet the expectations or projections disclosed in the forward-looking statements and you should not place undue reliance on these forward-looking statements. Such statements are based on management’s current expectations and involve risks and uncertainties. Actual results and performance could differ materially from those projected in the forward-looking statements as a result of many factors, including, without limitation, risks and uncertainties associated with the ability to project future cash utilization and reserves needed for contingent future liabilities and business operations, the availability of sufficient resources to fund our various product candidate development programs and to meet our business objectives and operational requirements, the fact that the results of earlier studies and trials may not be predictive of future clinical trial results, the protection and market exclusivity provided by our intellectual property, the substantial costs and diversion of management’s attention and resources which could result from pending securities litigation, risks related to the drug development and the regulatory approval process, including the timing and requirements of regulatory actions, and the impact of competitive products and technological changes. We disclaim any intent or obligation to update these forward-looking statements to reflect events or circumstances that exist after the date on which they were made. You should review additional disclosures we make in our filings with the Securities and Exchange Commission, including our Quarterly Reports on Form 10-Q and our Annual Report on Form 10-K. You may access these documents for no charge at http://www.sec.gov .

Investor Contacts:

Hans Vitzthum

LifeSci Advisors

Ph: 617-430-7578

hans@lifesciadvisors.com

Jim DeNike

Acer Therapeutics Inc.

Ph: 844-902-6100

jdenike@acertx.com

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