A polishing apparatus of a peripheral chamfered portion of a semiconductor wafer is disclosed. The polishing apparatus comprises: a rotary drum around the periphery of which a tape having an abrasive layer thereon is wound; a first motor for rotating the rotary drum; a wafer holding mechanism which comprises a wafer holding member for holding a wafer, a second motor for rotating the wafer holding member, a supporting member for supporting the wafer holding member and the second motor, and a wafer inclining member for changing the tilt angle of the wafer with respect to the rotary drum by reciprocally rotating the supporting member on a first axis which is substantially parallel with the main surface of the wafer; and a moving member for bringing the wafer held on the supporting member into contact with or separating it from the tape wound around the rotary drum.