US Edition Mr Trump, who is mulling a bid for the Republican presidential nomination, offered no proof for his claim but said he would continue to press the matter as he has the legitimacy of the president's birth certificate.
"I heard he was a terrible student, terrible. How does a bad student go to Columbia and then to Harvard?" Mr Trump said in an interview with The Associated Press. "I'm thinking about it, I'm certainly looking into it. Let him show his records."
Mr Obama graduated from Columbia University in New York in 1983 with a degree in political science after transferring from Occidental College in California. He went on to Harvard Law School, where he graduated magna cum laude 1991 and was the first black president of the Harvard Law Review.
Mr Obama's 2008 campaign did not release his college transcripts, and in his bestselling memoir, "Dreams From My Father," Mr Obama indicated he hadn't always been an academic star. Mr Trump told the AP that Mr Obama's refusal to release his college grades were part of a pattern of concealing information about himself.
"I have friends who have smart sons with great marks, great boards, great everything and they can't get into Harvard," Mr Trump said. "We don't know a thing about this guy. There are a lot of questions that are unanswered about our president."
Katie Hogan, a spokeswoman for Mr Obama's re-election campaign, declined to comment.
Mr Trump has shaped himself as an ultraconservative candidate, reversing some positions he once held. He now would make abortion illegal, opposes gay marriage and gun control. He advocates repeal of Mr Obama's health care overhaul that became law last year. He wants to cut foreign aid, is highly critical of China's trade and monetary policies and wants to end the U.S. wars in Iraq and Afghanistan.
But he has got the most political traction by latching onto the "birther" movement: those who believe claims initiated by the far-right that Mr Obama was born outside the United States – despite the release of official birth records in Hawaii and other evidence. The U.S. Constitution requires that presidential candidates be "natural-born" U.S. citizens.
Of late, Mr Trump has appeared in interviews on all the major American cable television networks, pushing relentlessly his message that Mr Obama needs to prove he was born in the United States. He points to his rising poll numbers as proof that Americans like what he is saying on that deeply divisive issue.
"I have more people that are excited about the fact that I reinvigorated this whole issue," Mr Trump said, adding "the last guy (Obama) wants to run against is Donald Trump."
Mr Trump is scheduled to travel to the early primary states of New Hampshire and Nevada this week and said he will make a final decision about a presidential bid by June.