Climpson is a surname of English origin. Notable people with the surname include:
Mary Janet Climpson (died 1940), British Salvation Army officer interred in Dieppe Canadian War Cemetery Roger Climpson (1931–2025), British-born Australian journalist, newsreader and television presenter
Fictional characters Miss Katharine Climpson, fictional character, elderly spinster, colleague of Lord Peter Wimsey in several detective novels by Dorothy L. Sayers
See also Clemson (disambiguation) Clempson