Isaac was the son of Andrew and Sarah Oakley Graham.

Isaac married Laura Goodrich Giraud, June 28, 1843, in New York City.

Isaac was in the wholesale drug business with his father and brother, operating as Graham & Company Wholesale Drugs.

Isaac encounterd financial difficulties and left his wife and son, traveling to Havana, Cuba, where he died of Yellow Fever June 20, 1856. His burial spot in Havana is still unknown.