J. Alexanders (JAX) 8-K J. Alexander’s Enters into Cooperation Agreement with Ancora Advisors

Exhibit 99.1

FOR IMMEDIATE RELEASE

J. Alexander’s Enters into Cooperation Agreement with Ancora Advisors

Appoints New Independent Director Carl J. Grassi to its Board of Directors

NASHVILLE, TN, April 20, 2020 — J. Alexander’s Holdings, Inc. (NYSE: JAX) (the “Company”), owner and operator of J. Alexander’s, Redlands Grill, Stoney River Steakhouse and Grill and other restaurants, today announced the expansion of its Board of Directors (the “Board”) to seven directors and the appointment of Carl J. Grassi to the Board as part of a cooperation agreement (the “Agreement”) with Ancora Advisors, LLC (“Ancora”). Mr. Grassi will serve as a Class II director, with an initial term through the Company’s 2020 Annual Meeting of Shareholders (the “2020 Annual Meeting”), and the Company has agreed to include Mr. Grassi in the Company’s slate of director nominees for election at the 2020 Annual Meeting for a three-year term.

“We are pleased to welcome Carl to the Board,” said Lonnie J. Stout II, Executive Chairman of the Board. “We believe his insight will be an asset as we move forward with the Company’s previously announced review of strategic alternatives, which we plan to continue once theCOVID-19-related uncertainties in the business community, the restaurant industry and the financial markets are resolved and the Company’s performance has returned to levels which will support an attractive valuation.”

“We anticipate that Carl will bring a unique perspective to the boardroom and support the Company’s efforts to enhance shareholder value,” added Mark Parkey, President and Chief Executive Officer of the Company.

Mr. Grassi is a Member at business advisory and advocacy law firm McDonald Hopkins, LLC (“McDonald Hopkins”) and serves on its Board of Directors. Mr. Grassi was firm chairman from 2016 to 2019 at McDonald Hopkins after serving as firm president for nine years. Mr. Grassi is corporate counsel to a number of middle-market and growth companies. He has extensive experience assisting clients with corporate law and tax law matters. Mr. Grassi earned a J.D. from Cleveland-Marshall College of Law in 1984. He received a B.S.B.A. from John Carroll University in 1981. Mr. Grassi is a member of the Advisory Board of Ancora Holdings Inc.

Fred DiSanto, Chairman and Chief Executive Officer of Ancora, said, “We are pleased to have reached this agreement with J. Alexander’s to add Carl to the Board. We look forward to continuing our collaborative engagement with the Board and management team to drive long-term value creation for shareholders.”

Under the terms of the Agreement, Ancora and its affiliates have agreed to abide by customary standstill and voting provisions until the earlier of (i) the 60th day prior to the Company’s 2021 Annual Meeting of Shareholders and (ii) the day immediately following any public announcement by the Company that it has abandoned its previously announced strategic review process. The Agreement will be included as an exhibit to the Company’s current report on Form8-K, which will be filed with the Securities and Exchange Commission.

About J. Alexander’s Holdings, Inc.

J. Alexander’s Holdings, Inc. is a collection of restaurants that focus on providing high quality food, outstanding professional service and an attractive ambiance. The Company presently operates 47 restaurants in 16 states. The Company has its headquarters in Nashville, TN.

For additional information, visit www.jalexandersholdings.com.

About Ancora Advisors, LLC

Ancora Advisors, LLC, is a registered investment adviser with the Securities and Exchange Commission of the United States. Ancora offers comprehensive investment solutions for institutions and individuals in the areas of fixed income, equities, global asset allocation, alternative investments and retirement plans.

Forward-Looking Statements

This press release containsforward-looking statements, which include all statements that do not relate solely to historical or current facts, such as statements regarding our expectations, intentions or strategies regarding the future, including the Company’s plans to continue its review of strategic alternatives and its efforts to enhance shareholder value. Theseforward-looking statements are based on management’s beliefs, as well as assumptions made by, and information currently available to, management. Because such statements are based on expectations as to future financial and operating results and other events and are not statements of fact, actual results may differ materially from those projected and are subject

2

to a number of known and unknown risks and uncertainties, including the health and financial effects of theCOVID-19 outbreak; the Company’s ability to reopen its restaurants forin-person dining, and thereafter to reestablish and maintain satisfactory guest count levels and maintain or increase sales and operating margin in its restaurants under varying economic conditions; the effect of higher commodity prices, unemployment and other economic factors on consumer demand; increases in food input costs or product shortages and the Company’s response to them; the number and timing of new restaurant openings and the Company’s ability to operate them profitably; competition within the casual dining industry and within the markets in which our restaurants are located; adverse weather conditions in regions in which the Company’s restaurants are located; factors that are under the control of third parties, including government agencies; the Company’s evaluation of strategic alternatives; as well as other risks and uncertainties described under the headings“Forward-Looking Statements,” “Risk Factors” and other sections of the Company’s Annual Report on Form10-K filed with the Securities and Exchange Commission on March 13, 2020, as amended on April 17, 2020, and subsequent filings. The Company undertakes no obligation to update anyforward-looking statements, whether as a result of new information, future events or otherwise.

Contacts:

J. Alexander’s Holdings, Inc.

Jessica Hagler

Chief Financial Officer

(615)269-1900

Ancora Advisors, LLC

James Chadwick

(216)593-5048

3