John W. Hinckley Jr., who was found not guilty by reason of insanity of attempting to assassinate President Reagan, says he now has "great remorse for the pain I inflicted on so many people" in "a crazy assassination attempt."

"I am very sorry for the shooting," Hinckley said in an "open letter" to Reagan, which Hinckley sent to The Washington Post. "I thank God no one died, but I still live with the fact that James Brady is partially paralyzed and his life is less than what it should be. The emotional pain that I caused is also tremendous, and I know your wife and family suffered greatly.

"I can only hope you and your family will forgive me for my past madness. I pray for the victims of the shooting every night, and God has been answering my prayers," Hinckley wrote.

Dr. Harold Thomas, a spokesman for St. Elizabeths Hospital, where Hinckley is confined, verified the authenticity of the letter. Thomas said the hospital screens Hinckley's mail but does not endorse his letter, nor did hospital officials suggest he write it.

Hinckley asked The Post to publish the letter on the anniversary of his March 30, 1981, assassination attempt. Addressed "Dear Mr. President," Hinckley opened the letter by saying, "Three years ago I shot you and three other men in a crazy assassination attempt."

Hinckley said he had written Reagan a similar letter a year ago but "all I got for my efforts was a visit by the Secret Service."

Saying he wants Reagan "and the rest of the country to please forgive me for my crime," Hinckley added, "I was mentally ill when I pulled the trigger and not responsible for my actions.

"On March 30, 1981, I was a different person than I am today. Three years of therapy and love has made all the difference in the world," he wrote.

Hinckley, who wrote the letter by hand on yellow, ruled paper, said his life at the hospital "is good right now" and "I'm getting well." He added, "I spend my days writing poems and playing my guitar, and I've never been so happy in my whole life."

Thomas, the hospital spokesman, said Hinckley is undergoing an "active therapeutic program" at the John Howard Pavilion at the hospital and that Hinckley and his attorney can ask for review of his case every six months. Hinckley made an apparent suicide attempt at St. Elizabeths on Feb. 13, 1983.

Thomas said Hinckley writes letters frequently. His telephone contacts are restricted to immediate family and attorneys.

Reagan said in an interview with The Post a year ago that he bears no grudge toward Hinckley. "I just think it would be fine if he could be cured, also," the president said.

Reagan has sent Congress legislation that would abolish the plea of not guilty by reason of insanity.