Born in Christchurch, New Zealand, from a young age Graham benefited from New Zealand's rich musical education system, playing with the Christchurch Youth Orchestra, Christchurch Symphony Orchestra, the New Zealand National Youth Orchestra and the New Zealand Symphony Orchestra. In 1975, at the age of 19, Graham was appointed Principal Timpanist of the Tasmanian Symphony Orchestra in Hobart, Australia, the youngest ever Principal player in the country at that time.
In 1983 Graham was appointed as Section Leader Percussion of the Royal Liverpool Philharmonic, where he currently performs under Maestrol Vasily Petrenko. On a number of occasions he has performed as soloist with the RLPO including the UK premiere of Takemitsu 'Gitimalya' for marimba and orchestra (broadcast live on BBC Radio 3) along with other well known solo works for percussion by Bartok, Milhaud and Panufnik. He continues to be invited to play with several of the UK's leading symphony orchestras.
In 1995, by special invitation, Graham became a founding member of the World Orchestra for Peace conducted by Sir George Solti. Currently conducted by Valerie Gergiev, this exceptional ensemble performs regularly at the BBC Proms in London and around the world as 'Ambassadors for Peace', with tours throughout Europe, Russia, China and the USA.