Algazi () is a Sephardi Jewish surname. People with the surname include: Hayyim Isaac Algazi (died 1819), rabbi Hayyim ben Menahem Algazi (17th century), rabbi Israel Yaakov Algazi (1680–1757), rabbi Solomon Nissim Algazi (1610 – c. 1683), rabbi Yom Tov Algazi (1727–1802), rabbi