A polishing apparatus for polishing a workpiece such as a semiconductor wafer has a turntable with a polishing cloth mounted on an upper surface thereof, and a top ring for holding a workpiece and pressing the workpiece against the polishing cloth under a first pressing force to polish the workpiece. The top ring has a recess defined therein for accommodating the workpiece therein. A presser ring is vertically movably disposed around the top ring, and is pressed against the polishing cloth under a variable second pressing force. The first and second pressing forces are variable independently of each other, and the second pressing force is determined based on the first pressing force. Relative rotation between the top ring and the presser ring is achieved during polishing.