Morrison was lead singer for top 1960s rock act The Doors and a Florida native. He was appealing the indecent exposure and profanity conviction when he died in 1971 in a Paris bathtub at age 27.
Crist told the St. Petersburg Times Tuesday that the more he looked into what happened that night, the more he thought it was right to seek a pardon. Morrison was fined and sentenced to six months in jail but never served that time.
A message left by The Associated Press with Crist's spokesman wasn't immediately returned.
Crist, a Republican-turned-independent, lost his bid for a U.S. Senate seat earlier this month.