A New South Wales representative goal-kicking fullback, he played club football in the NSWRFL Premiership for Sydney's St. George (with whom he won 5 consecutive grand finals) and Newtown.
In 1959 Graham gained his first representative honours when he was selected to play at fullback for the City New South Wales rugby league team in their 37–7 victory against Country.
He was the 1960 NSWRFL season's top points scorer, and he landed five goals in Saints' 31–6 win against Eastern Suburbs in the premiership decider.
In the 1961 ANZAC Day game against Eastern Suburbs Graham sealed his side's win with a 79th-minute penalty in front of 19,386 spectators at the SCG.
[3] He continued playing for St. George in 1964, surpassing Doug Fleming's point scoring record for the club,[4] but after receiving offers from Newtown and Manly-Warringah in early 1965[5] was transferred to the former for £1,000.