Born in East Haven, Connecticut, Plumb immigrated to Canada in 1865 and settled near Niagara Falls, Ontario.

He was elected three times as a member of parliament for Niagara in the House of Commons of Canada.

He was first elected in the Canadian federal election of 1874, but this result was voided, although he successfully defended the seat in a by-election held on 22 December 1874.

Following a defeat in 1882 election, he was appointed to the Senate of Canada on 8 February 1883 on the recommendation of Sir John A. Macdonald.

He served as Speaker of the Senate from 4 April 1887 – 12 March 1888, upon his death.