A polishing apparatus capable of precisely controlling a polishing profile, particularly a polishing profile in an edge portion, of a wafer is disclosed. The polishing apparatus includes: a top ring shaft; a housing fixed to the top ring shaft; a flexible membrane configured to press a wafer against a polishing pad; a top ring body configured to hold the flexible membrane; a retaining ring coupled to the top ring body and disposed so as to surround the flexible membrane; a gimbal mechanism configured to allow the top ring body and the retaining ring to tilt with respect to the housing; and a local load exerting mechanism configured to exert a downward local load on a part of the retaining ring.