A polishing unit of a polishing apparatus according to an embodiment includes: a polishing head having a pressing member configured to hold a polishing tape and press the polishing tape against a peripheral portion of a substrate from above; a tape supply and recovery mechanism configured to supply the polishing tape to the polishing head and recover the polishing tape from the polishing head; a first moving mechanism configured to move the polishing head in a radial direction of the substrate; and a second moving mechanism configured to move the tape supply and recovery mechanism in the radial direction of the substrate. The positioning unit includes a positioning block having a contacting surface, and alignment of the polishing tape is conducted by the second moving mechanism moving the tape supply and recovery mechanism so that a substrate-side edge of the polishing tape makes contact with the contacting surface.