Compston is a surname. Notable people with the surname include:
Alastair Compston (born 1948), Professor Emeritus of Neurology
Archie Compston (1893–1962), English professional golfer
Joshua Compston (1970–1996), British gallerist
Martin Compston (born 1984), Scottish actor
Peter Compston KCB (1915–2000), Royal Navy officer
Robert J. O. Compston DSC, DFC (1898–1962), English fighter pilot
William Compston (born 1931), Australian geophysicist
