Andrew or Andy Thompson may refer to:

• Andrew Thompson (catcher) (1846–?), Major League Baseball player for the 1875 Washington Nationals
• Andrew Thompson (footballer) (born 1972), Australian rules footballer
• Andrew Thompson (manager) (1845–1895), Major League Baseball manager for the 1884 St. Paul Saints
• Andrew Thompson (racing driver) (born 1987), Australian racing driver
• Andy Thompson (baseball) (born 1975), former Major League Baseball left fielder
• Andy Thompson (footballer, born in Sunderland) (fl. 1904–05), English football winger for Sunderland
• Andy Thompson (footballer, born 1899) (1899–1970), English footballer
• Andy Thompson (footballer, born 1967), English footballer
• Andrew Thompson (British racing driver) (active 2003–2004); see Hitech Racing

• Andrew Thompson (convict, magistrate) (c. 1773–1810), Australian convict and settler
• Andrew Thompson (historian) (born 1968), British historian specialising in modern empire
• Andrew Thompson (parasitologist), Australian parasitologist
• Andrew Thompson (politician) (1884–1961), Australian politician
• Andrew Green Thompson (1820–1889), British politician
• Andrew Thorburn Thompson (1870–1939), military officer, editor, lawyer and a third-generation political figure in Canada
• Andy Thompson (Canadian politician) (1924–2016), Canadian politician
• Andy Thompson (Ohio politician) (1963–2020), American politician
• Andy Thompson (theatre professional) (born 1970), Canadian entertainer

• Andrew Thomson (disambiguation)
• Andy Thomson (disambiguation)