The 62-year-old actor, who made his name in Cheers, said he had to identify the body of his teenage sister Karen after she was murdered.
The 18-year-old was abducted, raped, and murdered in Colorado by spree killer Freddie Glenn in 1975.
Glenn is currently serving a life sentence in prison.
Speaking of a life peppered with tragedy, Grammer told Desert Island Discs: “I have learnt to forgive. I have even told the guy that killed her that I do forgive him.
“You are just left with it, so I cherish her memory and the great love that we had and I continue to carry the joy that I felt in knowing her with me.”
Glenn was up for parole in 2009, but Grammer delivered an emotional testimony at the killer’s parole hearing.
He told Kirsty Young of his dread of seeing Glenn in public: “The punishment shouldn’t be worse for the family than it is for the guy that killed.”
The murder of his sister was not the first tragedy to strike the family. After his parents split when he was two, his grandfather took on a parental role, but died when Grammer was 12.
At 13, his estranged father Frank Allen Grammer was murdered – shot by a psychopath. And at 25 his two young half-brothers, Stephen and Billy, died in a scuba-diving accident.
The actor rose to fame in 1984 when he began playing psychiatrist Frasier Crane on NBC’s Cheers and went on to star in 11 series of offshoot Frasier. He has won 37 Emmys, a Tony and three Golden Globes.
He is currently in London’s West End show Big Fish: The Musical. His song choices included Frank Sinatra’s Fly Me To The Moon and Jimi Hendrix’s All Along The Watchtower.
His book of choice was A Passage To India by EM Forster and a magnifying glass was his luxury item.
Desert Island Discs, today, Radio 4, 11.15am.