Adam was born in Telfair County, Georgia, to Alexander and Mary or Sarah Smith Graham. A merchant of Valdosta, Georgia, he served as a 2nd lieutenant in Company I of the 12th Regiment Georgia Volunteers and eventually became captain of his company. Adam lost a hand, was wounded in the leg, and was captured by Union forces in July 1864. He was incarcerated in a Union Army hospital and died in Fort Delaware, 23 Apr. 1865.