A polishing apparatus polishes a periphery (a bevel portion, a notch portion, an edge-cut portion) of a substrate by bringing a polishing tool into sliding contact with the periphery of the substrate. The polishing apparatus includes a substrate holder configured to hold the substrate, and a polishing head configured to polish the periphery of the substrate held by the substrate holder using the polishing tool. The polishing head includes a press pad for pressing the polishing tool against the periphery of the substrate, and a linear motor configured to reciprocate the press pad.