As an amateur, Spinks won numerous medals in the light heavyweight division. The first was bronze at the inaugural 1974 World Championships, followed by silver at the 1975 Pan American Games, and gold at the 1976 Summer Olympics; the latter alongside his brother Michael Spinks, who won middleweight gold. Leon served in the United States Marine Corps from 1973 to 1976, rising to the rank of corporal. He was stationed at Marine Corps Base Camp Lejeune in North Carolina and was on the Marine Corps Boxing Team.