Born in Sydney in 1949, commencing flute lessons with Victor McMahon at the age of eight. Changing instruments at age twelve, Graham studied oboe at the N.S.W, Conservatorium with Guy Henderson and composition with Raymond Hanson.
After completing his D.S.C.M. in 1970 Graham was appointed to the staff of the N.S.W. Conservatorium, and 1972 saw him joining the Elizabeth Sydney Orchestra as Principal Oboist. After receiving the Queen Elizabeth Jubilee Medal for his services to music in 1977, Graham was the first Australian oboist to be invited to give a lecture/recital at the Double Reed Convention held in Florida, U.S.A. in 1983.
Over the past twenty years his compositions have been written mainly for woodwind, and his great sense of humour shows through in the highly imaginative titles of his works.