[Object] An outer periphery polishing apparatus capable of polishing the edge of workpieces having different bevel angles is to be provided.[Solution] Edge polishing units 2A, 2B for polishing the front surface edge Ea and the rear surface edge Eb of the workpiece W each include a polishing member mounting structure 11 to which a polishing member 10 is attached, a mounting structure support unit 12 that tiltably supports the polishing member mounting structure 11, a mounting structure angle adjustment mechanism 13 that adjusts a tilt angle of the polishing member mounting structure 11, a reciprocation support base 15 that supports the mounting structure support unit 12 so as to move along a reciprocation line, a base support unit 17 that tiltably supports the reciprocation support base 15, a base angle adjustment mechanism 18 that adjusts the tilt angle of the reciprocation support base 15 so as to be parallel to the edge Eb of the workpiece W, and a pedestal 19 that supports the base support unit 17 so as to allow positional correction in a vertical direction and a horizontal direction.