A polishing apparatus comprises a polishing plate (24), an abrasive cloth (25) attached to the surface of the polishing plate (24), a chuck (19) for holding and pressing one surface of a wafer (39) against the abrasive cloth (25), and a circular retaining ring (23) concentrically arranged on the periphery of the chuck (19). The retaining ring (23) is rotatable and vertically movable with respect to the chuck (19), and is pressed against the abrasive cloth (25) during the lapping step. The retaining ring (23) is lifted upward during the final polishing step, thereby preventing lapping grains from being brought into the final polishing stage. Accordingly, lapping and final polishing can be successively conducted using the same polishing head. With this structure, cost cutting of the apparatus can be realized, since lapping and final polishing are successively conducted using the same polishing head without bringing the lapping grains used for lapping into the final polishing stage.