Burleigh Martin (September 3, 1888 – March 23, 1962) was an American politician from Maine.
From 1923 to 1928, Martin served in the Maine House of Representatives.
Elected to the Maine Senate in 1928, Martin served until 1932.
During his final term (1931–1932), Martin was elected Senate President.
Brann was the first Democrat elected Governor of Maine since Oakley C. Curtis in 1914.