President-elect Donald Trump’s charitable foundation engaged in self-dealing in 2015 and prior years, the foundation said in an Internal Revenue Service filing.

That self-dealing, which typically triggers additional taxes for anyone who got improper benefits, resulted from payments to “disqualified persons,” or foundation insiders, according to the document. The document, which was the foundation’s tax return for 2015, doesn’t provide more details. Representatives for Mr. Trump didn’t respond to requests for comment Tuesday.

The tax form asks if any income or assets were transferred to a disqualified person, and the foundation checked “yes.” The signed, undated form was posted on Guidestar, a website that compiles nonprofits’ tax forms. Guidestar said it was submitted by the law firm representing the foundation and that it might not be the exact final version that gets submitted to the government.

“They admit at this point that there are problems with their prior returns,” said Phil Hackney, a Louisiana State University law professor who has been examining the returns.

The tax code requires nonprofits to release their tax returns publicly. As a result, the foundation’s filings give voters one of the few peeks they have had into Mr. Trump’s dealings with the IRS. He was the first major-party presidential candidate in 40 years to refuse to release his tax returns.

Trump’s private foundation is relatively small compared to other large nonprofits. Its total expenditures were less than $1 million in 2015, less than 1% of the expenditures of the Bill, Hillary and Chelsea Clinton Foundation.

The foundation is a tiny piece of Mr. Trump’s financial network, which includes branding deals around the globe, golf courses and Manhattan real estate. Those business ties are fueling concerns about conflicts of interest with his duties as president.

Mr. Trump has said he would give control of his businesses to his children, but he could still take official actions that would benefit himself because conflict-of-interest laws don’t apply to the president.

Mr. Trump’s foundation has already admitted that it made an improper donation to a political group associated with Florida Attorney General Pam Bondi in 2013, essentially making a payment that should have been from Mr. Trump’s pocket directly.

The new disclosure may cover more issues than that payment because it acknowledges problems in 2015. The Washington Post has outlined several possible instances of self-dealing, including foundation funds being used to purchase a painting of Mr. Trump displayed in one of his clubs and money being used to settle business lawsuits.

Typically, when a foundation reports self-dealing, the insiders pay the penalties to the government, and repay the foundation with interest. Those payments typically come with a separate nonpublic tax return. Foundations also sometimes reach an agreement with the IRS, said Lloyd Mayer, a tax law professor at the University of Notre Dame.

“It is resolved almost always civilly,” he said. “You pay the amounts. You repay the foundation. Maybe the foundation takes some steps to make sure this doesn’t happen again.”

Self-dealing with a private foundation typically triggers a 10% excise tax or a 200% excise tax if there is a failure to correct past self-dealing, said Suzanne Ross McDowell, a nonprofit tax lawyer at Steptoe & Johnson LLP in Washington.

“The self-dealing rules are highly technical, and it’s not unusual for foundations to unknowingly engage in self-dealing,” she said. “Many small family foundations do not fully understand the rules.”

An IRS spokesman said the law prevents the agency from commenting on specific tax return information or say whether it’s investigating any particular organization. The New York state attorney general’s office, which regulates charities, continues to investigate Mr. Trump’s Foundation.

Mr. Trump is the president of the foundation and his three oldest children are on the board of directors; the foundation doesn’t pay them directly. Unlike in previous years, Mr. Trump’s signature wasn’t on the form.

Mr. Trump’s companies donated to the foundation in 2015, giving more than $600,000 and breaking with his recent history of relying mostly on other people’s money for the foundation, the tax filing showed.

Recipients of the foundation’s money in 2015 included conservative groups such as the Media Research Center, the American Conservative Union Foundation and Project Veritas, the group founded by James O’Keefe that releases undercover videos. Other recipients included the Apollo Theater Foundation, the Leukemia and Lymphoma Society and the New Jersey Boxing Hall of Fame.

The Trump foundation also reported receiving a donation of $150,000 from the foundation of Victor Pinchuk, a Ukrainian businessman.

The payment was “in support” of a video appearance by Mr. Trump in September 2015 at a conference sponsored by the Pinchuk foundation and Yalta European Strategy, another group Mr. Pinchuk founded, Thomas Weihe, head of the foundation’s board, said in an email on Tuesday.

Mr. Pinchuk organizes the Davos-like conference each year. Mr. Trump said he had known Mr. Pinchuk for a long time and praised the Ukrainian tycoon as a “special entrepreneur” and a “tremendous guy.”

Despite his statements about Russian President Vladimir Putin that have upset Ukrainians, Mr. Trump criticized President Barack Obama in the video-link appearance for being too weak and not doing right by Ukraine.

“Part of the problem that Ukraine has with the United States is that Putin does not respect our president whatsoever,” Mr. Trump said, saying he had very strong feelings toward Ukraine and lots of friends there.

Mr. Pinchuk, a Ukrainian tycoon married to the daughter of former Ukrainian President Leonid Kuchma, is one of the country’s highest-profile philanthropists, contributing to the arts in Ukraine and to an array of causes outside the country.

“Mr. Pinchuk had met Mr. Trump some years ago in New York,” Mr. Weihe said. “This is how the invitation for Mr. Trump to speak at the YES meeting came about.”

Mr. Pinchuk’s foundation gave at least $8.6 million to Bill and Hillary Clinton’s foundation, contributing to the conflict-of-interest concerns that Mr. Trump raised during the presidential campaign. Mr. Pinchuk, whose fortune stems from a pipe-making company, served two terms as an elected member of the Ukrainian Parliament.

Mr. Trump now faces some of the same conflict-of-interest questions that Mrs. Clinton did because of the opacity of his finances and the breadth of the president’s powers and ability to assist his own business interests.

Because it can get routine extensions from the IRS, Mr. Trump’s foundation likely won’t file its returns for 2016 until November 2017. That means the public won’t know who donated to him during the presidential campaign and the transition until after he is in office.

“You’ll eventually know, assuming that they’re being forthright,” Mr. Hackney said. “So there is reporting here that’s a lot more transparent than contributions to the Trump Organization itself, which we can’t see or know about, ever.”

The form also discloses, with no detail, that the foundation made $41,636 in “other nondeductible charitable contributions.” That’s odd, Mr. Mayer said, because the foundation wouldn’t take deductions anyway.

“I’m not saying that it’s flatly wrong to have listed it this way,” he said. “But it’s pretty cryptic.”

Write to Richard Rubin at