Dr. Grissom was born in Granville County, N.C. In his youth, he studied law, taught school, and, at the age of 22, was elected clerk of his local court. He studied medicine at the University of Pennsylvania, receiving the M.D. degree in 1858. During the Civil War, he volunteered and served as a captain of the North Carolina Company. He was elected to the N.C. legislature for two terms and also appointed by the governor as Assistant Surgeon General of North Carolina.
In 1868, Dr. Grissom became Superintendent of the Raleigh Insane Asylum, a post he retained until 1889. Dr. Grissom received an honorary L.L.D. from Rutherford College in 1877. He wrote on insanity and medical-legal subjects, including a paper on “True and False Experts,” which engaged in a controversy with William Hammond, M.D., Surgeon General of the U.S. Army. Dr. Grissom was President of the Association of Medical Superintendents of American Institutions for the Insane (1887–1888).