Graham was born in Selkirkshire, Scotland, the son of William Graham and Lillias Riddell, and was educated at Aslekirk, Selkirk and Heriot, Midlothian. He came to Canada in 1890, and worked as a farmer and livestock importer. In 1892, Graham married Elizabeth Heattie. For many years, he was the Manitoba vice-president on the Board of the Clydesdale Horse Association. Graham resided in Carberry during his political career, and was a Presbyterian in religion.^[2]

He was first elected to the Manitoba legislature in the 1914 provincial election, defeating incumbent Conservative Robert F. Lyons^[1] by sixty-eight votes in the constituency of Norfolk. The Conservatives won this election, and Graham sat as a member of the opposition.

In early 1915, the Conservative administration of Rodmond Roblin was forced from office amid a corruption scandal. A new election was called, which the Liberals won in a landslide.^[3] Graham was personally re-elected, defeating Lyons^[1] by 163 votes. For the next five years, he served as a backbench supporter of Tobias Norris's administration. He was defeated in the 1920 election, losing to Conservative Reuben Waugh^[1] by 217 votes.

He died at home in St. Vital in 1951.^[2]