EXHIBIT 99.1

For Immediate Release

J. Robert Paulson and Jeffrey Mathiesen Appointed to Sun BioPharma Board of Directors

Two Experienced Healthcare Executives Join Board as Company Prepares to Enroll First Patient in Phase 1 Clinical Trial

Minneapolis, MN, September 30, 2015- Sun BioPharma, Inc., (OTCPink: SNBP), a biopharmaceutical company developing therapies for pancreatic diseases, today announced the appointment of healthcare executives J. Robert Paulson and Jeffrey Mathiesen to the Company’s Board of Directors. The appointments are effective immediately and bring the number of directors to 8 members, of which 4 are independent.

“The expansion of Sun’s board of directors is part of the Company’s effort to emphasize our commitment and accountability to shareholders and proper corporate governance practices,” said Dr. Michael T. Cullen, Executive Chairman of Sun BioPharma. “Bob’s leadership and operational experience in the healthcare field coupled with Jeff’s international, capital markets and financial management accumen make them highly qualified to be members of our board. We look forward to their contributions and guidance as we begin the Phase 1 clinical study for our lead development candidate, SBP-101, in Australia which we hope to initiate before the end of this year.”

J. Robert Paulson currently serves as President and CEO of NxThera Inc., a Maple Grove, MN based medical device company pioneering the application of its Convective Water Vapor Energy (WAVE™) platform technology to treat endourological conditions. Previously, Mr. Paulson was president, chief executive officer and a director of Restore Medical from 2005 until the company’s acquisition by Medtronic in July of 2008 and served as the chief financial officer and vice president of global marketing for Endocardial Solutions, which was acquired by St. Jude Medical in 2005. Mr. Paulson received a JD from Vanderbilt University School of Law, MBA from the University of St. Thomas, and BA from Luther College.

Jeffrey Mathiesen is Chief Financial Officer of Gemphire Therapeutics Inc., a Northville, MI based biopharmaceutical company focused on developing and commercializing therapies for the treatment of dyslipidemia. Prior to joining Gemphire Therapeutics, Mr. Mathiesen served as CFO of Sunshine Heart, Inc., leading the medical device company through its transition from the Australian capital markets to the U.S., which included a successful IPO and equity financings totaling approximately $100 million. Mr. Mathiesen has more than 20 years of experience as CFO of publicly traded companies, including two successful initial public offerings, encompassing a variety of highly competitive, technology based industries in organizations with global reach. Mr. Mathiesen graduated summa cum laude in Accounting from the University of South Dakota.

Mr. Paulson will serve as Chair of Sun BioPharma’s Corporate Governance Committee and become a member of the Compensation Committee, while Mr. Mathiesen will serve as Chair of the Audit Committee and become a member of the Governance Committee.

About Sun BioPharma

Sun BioPharma, Inc. is a next-generation biopharmaceutical company developing disruptive therapeutics for serious unmet medical needs. The company’s initial programs are aimed at diseases of the pancreas, including pancreatitis and pancreatic cancer, and the Company’s lead clinical program is SBP-101. Sun BioPharma has scientific collaborations with pancreatic disease experts at The Ohio State University, the Fred Hutchinson Cancer Center in Seattle, Translational Genomics (TGen) in Scottsdale, AZ, Cedars Sinai Medical Center in Los Angeles, the University of Minnesota, the Austin Health Cancer Trials Centre, the Box Hill Hospital in Melbourne, Australia and the Ashford Cancer Centre in Adelaide, Australia. Further information can be found at: www.sunbiopharma.com.

About SBP-101

SBP-101 is a first-in-class proprietary polyamine compound designed to exert therapeutic effect in a mechanism specific to the pancreas. Sun BioPharma originally licensed SBP-101 from the University of Florida in 2011. The molecule has been shown to be highly effective in human pancreatic cancer models, demonstrating superior activity to existing chemotherapy agents. Combination potential has also been shown for pancreatic cancer. SBP-101 is expected to hold an edge over current pancreatic cancer therapies, since it specifically targets the exocrine pancreas and may eliminate both primary and metastatic pancreatic cancer, while leaving the insulin-producing islet cells and non-pancreatic tissue unharmed.

Safe Harbor

Statements pertaining to future financial and/or operating results, future growth in research, technology, clinical development, and potential opportunities for Sun BioPharma, along with other statements about the future expectations, beliefs, goals, plans, or prospects expressed by management constitute forward-looking statements. Any statements that are not historical fact (including, but not limited to statements that contain words such as “will,” “believes,” “plans,” “anticipates,” “expects,” “estimates”) should also be considered to be forward-looking statements. Forward-looking statements involve risks and uncertainties, including, without limitation, risks inherent in the development and/or commercialization of potential products, uncertainty in the results of clinical trials or regulatory approvals, need and ability to obtain future capital, and maintenance of intellectual property rights. Actual results may differ materially from the results anticipated in these forward-looking statements and as such should be evaluated together with the many uncertainties that affect the businesses of Sun BioPharma particularly those mentioned in the cautionary statements found in Sun BioPharma’s filings with the Securities and Exchange Commission. Sun BioPharma disclaims any intent or obligation to update these forward-looking statements.

Contact Information:

EVC Group

Investor Contact:

Doug Sherk

415-652-9100

Michael Polyviou

212-850-6020

Media Contact:

Dave Schemelia

646-201-5431

Source: Sun BioPharma Inc.

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