A polishing apparatus for polishing a workpiece such as a semiconductor wafer has a turntable with an abrasive cloth mounted on an upper surface thereof, and a top ring for holding a workpiece and pressing the workpiece against the abrasive 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 pressed against the abrasive 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.