Henry Joseph Graham was born September 7, 1913 in Boerne, Texas. His parents were Joseph H. Graham, a lawyer, and Elizabeth Orynski Graham, a prominent preservationist in San Antonio. Henry had one sister, Wanda Graham, who married architect O'Neil Ford. Graham married Carolyn Hoon (1914-1976) in 1938; they had two children, William Henry (1942-1960) and Carolee Graham.
In 1936 Henry and Carolyn Graham purchased and renovated the Weyrich Building, the oldest extent commercial building in Boerne, before selling it to Elizabeth Graham in 1944. Henry worked as an editor for the Time-Life Corporation. In the 1960s, Henry was a central figure alongside his sister Wanda Ford in the opposition movement against the construction of the 281 freeway in San Antonio. As part of these efforts, he formed the Save Our City Organization.
Henry Graham died on September 21, 1997.