Swaby is a surname. Notable people with the surname include:
Allyson Swaby (born 1996), American-born Jamaican footballer Chantelle Swaby (born 1998), American-born Jamaican footballer Cyril Swaby (1905–1974), Anglican Bishop of Jamaica Donn Swaby (born 1973), American actor Gordon Swaby (born 1990), Jamaican internet entrepreneur Harry Swaby (1906–1982), English footballer James Swaby (1798–1863), Jamaican officer in the British Army James Swaby (priest) (1862–1944), Archdeacon of Belize Javid Swaby-Neavin (born 2001), English footballer Lee Swaby (born 1976), British boxer Mario Swaby (born 1982), Jamaican footballer Proctor Swaby (1844–1916), British-born colonial bishop
See also George Swabey (1881–1952), Royal Navy officer