Anzai (written: 安西, 安斎 or 安済) is a Japanese surname. Notable people with the surname include:
Atsuko Anzai (安西 篤子, born 1927), Japanese novelist
Chika Anzai (安済 知佳, born 1990), Japanese voice actress
Earl I. Anzai (born 1941), American lawyer and politician
Emma Anzai, Australian musician
Hiroko Anzai (安西 ひろこ, born 1979), Japanese actress, model and gravure idol
Fuyue Anzai (安西 冬衛, 1898–1965), Japanese poet
Nobuaki Anzai (安斎 伸彰, born 1985), Japanese Go player
Nobuyuki Anzai (安西 信行, born 1972), Japanese manga artist
Shigeo Anzai (安斎 重男, born 1939), Japanese photographer