Burleigh Martin was born in Augusta, Maine in 1889. He was educated at Cony High School and at Bowdoin College before studying law at Harvard. A member of the Augusta City Council in 1914, he served as City Clerk from 1915 to 1918 and as Mayor of Augusta from 1919 to 1920.
Elected to the Maine House of Representatives for three consecutive terms beginning in 1923, Martin was Speaker of the Maine House of Representatives in 1927. Elected to the Senate in 1929 he was reelected for the 1931-1932 term during which time he served as President of the Senate.