Crum was the eldest son of Walter Crum FRS of Thornliebank and his wife Jesse Graham, daughter of William Graham of Burntshiel, Renfrewshire. The Crum family were associated with the printworks which had been founded in Thornliebank in 1778. Crum's father Walter Crum was a chemist and businessman, who replaced the spinning and weaving business by calico printing. Crum ran the printworks, which was the main employment in the village, and he was also a major benefactor supporting housing, education, and leisure facilities in the village. He also provided funds for the village club and Thornliebank Parish Church. He was also a J.P. and deputy lieutenant of Renfrewshire.
Crum was elected unopposed as the Member of Parliament (MP) for Renfrewshire at a by-election in November 1880. He held the seat until the constituency was divided at the 1885 general election, when he did not stand again.
He died at the age of 65 and was commemorated by the library in Thormliebank, opened in 1897.
- Portal to the Past: East Renfrewshire's Heritage Collection – Thornliebank
- Debretts House of Commons and the Judicial Bench 1881
- "No. 24908". The London Gazette. 30 November 1880. p. 6351.
- Craig, F. W. S. (1989) . British parliamentary election results 1832–1885 (2nd ed.). Chichester: Parliamentary Research Services. p. 601. ISBN 0-900178-26-4.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "P" (part 2)