George Grigsby was a delegate to the state Democratic convention in 1896. During the Spanish–American War, he served as a lieutenant in the Third Regiment, United States Volunteer Cavalry. He moved to Nome, Alaska, in 1902. He was an assistant United States attorney from 1902 to 1908 and a United States attorney from 1908 to 1910. He was the city attorney of Nome in 1911 and the mayor in 1914. In 1915, he was a member of the board of commissioners for the promotion of uniform legislation. He was elected the first attorney general in 1916, and he resigned in 1919.
He presented his credentials as a Democratic Delegate-elect to the Sixty-sixth Congress to fill the vacancy caused by the death of Charles A. Sulzer. He served from June 3, 1920, to March 1, 1921, when he was succeeded by James Wickersham, who had contested the election of Charles Sulzer in the first instance and contested against George Grigsby. He was a delegate to the Democratic National Convention in 1920 and 1924. He engaged in the practice of law in Ketchikan, Juneau, and Anchorage, Alaska.
