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