Graham became a professional tennis player in the early 1980s. He specialized in men's doubles and reached his first double final on the ATP World Tour in 1983 . The following year he won his first double title in Newport . His second and final title followed in 1985, both alongside Laurie Warder . In addition to his two double titles, he was twice in a final. He reached his highest ranking in the tennis world rankings in 1983 with position 324 in singles and 1984 with position 46 in doubles.
He was only able to qualify for a Grand Slam tournament once, in 1982 he failed in the first round of Wimbledon . In the doubles competition he reached the semi-finals of the Australian Open in 1983 at the side of Laurie Warder , but they were defeated by the eventual tournament winners Mark Edmondson and Paul McNamee in straight sets.