He played for the St. Michael's Buzzers Junior "B" team in 1976-77 and then played for the Toronto Marlboros and the Niagara Falls Flyers from 1977 to 1981. In the 1980 NHL Entry Draft the Pittsburgh Penguins chose him 114th overall.
Graham turned pro with the Penguins in 1981-82 and scored 6 goals and 8 assists in 42 games. The next season he only played in 20 NHL games. The Toronto Maple Leafs traded for him in 1983 but he only played 41 games for them in 1983-84.
Graham finished off his career in 1984-85 playing in Germany.
In the NHL Graham played in 103 games and scored 11 goals and 17 assists.