A polishing apparatus is used for polishing a substrate such as a semiconductor wafer. The polishing apparatus includes a substrate holder to hold a substrate and to rotate the substrate, a pressing member configured to press a polishing tool against the substrate and to polish the substrate, a pressing force control mechanism configured to control a pressing force of the pressing member, and a polishing position limiting mechanism configured to limit a polishing position of the pressing member. A polishing tape or a fixed abrasive is used as the polishing tool.