R. Malcolm Graham was born in Parrott, Georgia. He received a B.A. degree from New York University, where he was awarded the Rudolf K. Brosius Key for Outstanding Achievement in Business Writing and Speaking, and a J.D. degree from Boston College Law School. From 1974 to 1982, he was in the private practice of law with a concentration in civil litigation, labor law, and administrative law.
Justice Graham was named to the District Court by Governor Edward King in 1982. He was a member of the stress management committee of the District Court and is coauthor and editor of Judicial Wellness: A Stress Management Guide For and By Judges, published in 1996 by the National Judicial College. Justice Graham was appointed to the Superior Court by Governor Michael Dukakis in 1986. There he served as chairman of the Appellate Division of the Superior Court, regional administrative judge for criminal business for Middlesex County, and member of the personnel committee. He was appointed to the Appeals Court by Governor Mitt Romney and took his seat on October 20, 2004. Justice Graham served for many years as a member of the executive committee of the Massachusetts Judges Conference and established its International Judicial Exchange Program.
He was awarded the MJC President's Award for Judicial Excellence. Justice Graham was also a Helm's All-American College Basketball Player and a member of two Boston Celtics world championship teams, is a member of the NYU Sports Hall of Fame, and was a recipient of the National Collegiate Athletic Association College Athletes Top Six Silver Anniversary Award. He lives west of Boston with his wife, Joyce (Jackson) Graham.