Born in Sampson County, North Carolina in 1896, he moved to Burgaw, North Carolina at the age of 12, where he attended public schools. During World War I, Barden was a seaman in the United States Navy.
After leaving the Navy in 1919, Barden attended the University of North Carolina at Chapel Hill, where he studied law and was admitted to the bar in 1920. After briefly practicing law and teaching high school that same year, he became a judge in the Craven County courts, a post he held until 1924.
In 1932, Barden was elected to the North Carolina House of Representatives; two years later, he won the first of thirteen consecutive terms in the United States House. During the 78th and 79th Congresses, he chaired the House Education Committee; after that committee merged to become the Education and Labor Committee, he again became chairman in the 81st, 82nd, 84th, 85th, and 86th sessions.
In 1979, Campbell University Press published a biography by Elmer L. Puryear.
Graham A. Barden Elementary School, in Havelock, North Carolina is named after him.