Graham was appointed Chairman of the Malaghan Institute Trust Board in 1990. He was first employed at General Foods Corp in 1967, and was appointed General Manager of Refrigerated Freight lines in 1970, acquiring the company in 1987. Graham was founding Chairman of Tasman Express Line and a member of the Land Transport Safety Authority for six years. In 2009 he was awarded an Honorary Doctorate of Science from Victoria University of Wellington for his key role in rebuilding the Malaghan Institute into the largest independent medical research organisation in New Zealand. Recipient of the Sir Bob Owens award in 2010 for contributions to the transport, logistics industries and the community, Graham was made an Officer of the Order of Merit for his services to medical research and philanthropy in 2012. His current directorships include several private companies.