Anstey is a surname. Notable people with the surname include:
Brendel Anstey, English footballer who played for Aston Villa and Leicester CityBruce Anstey, New Zealand motorcycle racerChris Anstey, Australian basketball playerChristopher Anstey (1724–1805), English writer and poetEdgar Anstey (1907-1987), English film makerF. Anstey pseodonym for Thomas Anstey Guthrie (1856–1934), an English novelist and journalist who wrote comic novels under the pseudonym F. AnsteyFrank Anstey, Australian politician in both the Victorian and Commonwealth parliamentsGeorge Alexander Anstey (1814–1895), South Australian viticulturist and Member of ParliamentHarry Anstey, Australian prospector and politicianNigel Anstey, British geophysicistThomas Chisholm Anstey, British parliamentarian, lawyer and second Attorney General of Hong Kong