A polishing apparatus according to the present invention is suitable for use in polishing a periphery of a substrate such as a semiconductor wafer. The polishing apparatus includes a holding section configured to hold the workpiece, a polishing head configured to bring the polishing tape into contact with the workpiece, a supply reel configured to supply the polishing tape to the polishing head, a rewind reel configured to rewind the polishing tape that has contacted the workpiece, and a swinging mechanism configured to cause the polishing head to perform a swinging motion with its pivot lying on a predetermined point.