Leo Randolph was a product of the Tacoma Boys Club amateur program, along with fellow Olympic Gold Medalist Sugar Ray Seales, and future world champions Rocky Lockridge and Johnny Bumphus. He was trained as an amateur and professional by Joe Clough, the head trainer at the Tacoma Boys Club.
He was inducted into the Tacoma-Pierce County Sports Hall of Fame in 2005.
As of March 2007, Randolph was working as a bus driver in Tacoma.
- Amateur Record: 160-7
- 1975 National Golden Gloves Flyweight Champion
- 1976 National AAU Flyweight Champion
- 1976 Olympic Flyweight Gold Medalist. Results:
- Named the Boxing Writers Association of America Fighter of the Year for 1976, along with his fellow U.S. Olympic Gold Medalist in boxing (Howard Davis Jr., Sugar Ray Leonard, Leon Spinks, and Michael Spinks).
| WBA Super Bantamweight Champion
1980 May 4 – 1980 Aug 9
Sergio Victor Palma