A polishing apparatus is used for polishing a workpiece such as a semiconductor wafer to a flat mirror finish by a combination of chemical polishing and mechanical polishing. The polishing apparatus includes a turntable with a polishing cloth mounted on an upper surface thereof, a top ring for supporting the workpiece to be polished and pressing the workpiece against the polishing cloth, and a dressing tool for dressing the polishing cloth on the turntable. The polishing apparatus further includes a cover which covers an upper surface of the turntable for preventing liquid on the turntable from being scattered, and inserting holes formed in an upper wall of the cover for inserting the top ring and the dressing tool therethrough.