Hayyim Isaac Algazi (; died 1819) was the Chief Rabbi of Smyrna in late 18th century.
Algazi authored: "Derek EẠhaḤayyim" (The Way of the Tree of Life), "<nowiki>'</nowiki>En Yamin" (The Right Eye), and "Sha'ar Yehudah" (The Gate of Judah); all published posthumously at Salonica in 1822.