The Jerusalem Post, which obtained the letter, reported Friday that Israeli President Shimon Peres handed it to Obama when he visited the White House April 5.
It is Pollard's first letter to a president since his arrest for passing U.S. secrets to Israel in 1985. He was sentenced to life in 1987 but is eligible for parole in 2015. Obama had not responded.
"I hope that my own personal appeal may touch your heart and elicit a compassionate, humanitarian response to my heartfelt request to be sent home to Israel for Passover, the holiday of freedom," Pollard wrote.
He cited his failing health and his wife Esther's cancer fight while expressing "deep regret" for his crimes. He also noted that a former CIA director and other prominent Americans back his release.
Israel granted Pollard citizenship after initially denying he was an agent.
Esther Pollard said Wednesday: "Obama's utter indifference to Peres' request was very puzzling but it has to be seen in context of the president's indifference to all of the requests he has received."