[1] A Republican, Graham served in local offices, including auditor for the village of Bellows Falls, and grand juror (municipal court prosecutor) for the town of Rockingham.

[1] During the governorship of Allen M. Fletcher, Graham served as his Secretary of Civil and Military Affairs (chief assistant).

[7] In 1931, Graham was appointed as an associate justice of the Vermont Supreme Court, filling the vacancy caused by the resignation of Julius A. Willcox,[8] and he served until his death.

[5] He had been ill with appendicitis, and died as the result of post-surgical complications including gangrene and peritonitis.

[11] Gordon Graham died while serving in the United States Army during World War II, perishing as a result of the sinking of the SS Dorchester.