Born in 1947, Graham was educated at Whitgift and Durham. He was ordained in 1977 and became Curate at All Saints, Tooting Graveney. Following this he was Team Vicar of St Paul's, Thamesmead, then Team Rector of Kidlington with Hampton Poyle, Oxford, becoming Rural Dean of Oxford in 1989.
In 1997 he became Team Rector of Leeds Parish Church and was made an Honorary Canon at Ripon Cathedral. In 2004 he was appointed Dean of Norwich.
Graham is married to Carys, who is a lecturer in education. They have three children. His interests include restoring old houses, theatre and cinema, biography and music.