Gleaves is a (patronymic or paternal) family name. Variant spellings include Gleave, Glave and Glares.
Notable people with this surname include:
Albert Gleaves (1858–1937), American admiral Richard Howell Gleaves (1819–1907), American lawyer, merchant and politician Nicholas Gleaves, English actor and playwright Sam Gleaves, English football manager
See also Gleaves-class destroyer, named after Admiral Gleaves , lead ship of the class