Astwood is a surname. Notable people with the surname include:
Cynthia Astwood (born 1946), British diplomat Edwin Astwood (born 1973), Turks and Caicos Islands politician Edwin B. Astwood (1909–1976), Bermudian-American physiologist and endocrinologist Glenn Astwood, (born 1954), Bermudian sailor Jeffrey Carlton Astwood (1907−1997), Bermudian politician Jeffrey Christopher Astwood (born 1933), Bermudian politician Norma Cox Astwood, Bermudian psychologist Stephen Astwood (born 1981), Bermudian football player William Marischal Astwood, Bermudian politician