An apparatus for chamfering the peripheral edge of a semiconductor wafer to specular finish, consisting of a turn table with an abrasive table surface, and a wafer holder, which holds the wafer firmly by sucking one face of the wafer, turn the wafer circumferentially, and press the wafer edge against the abrasive table surface in a manner such that the edge of the wafer is brought and kept in contact with the table surface in a way such that the triangle formed by the center of the turn table surface, the center of the wafer and said contact point is normal to the turn table surface and the angle formed between the turn table surface and the wafer is at the beginning substantially close to 0.degree. but said angle is continuously or stepwise increased to a value substantially close to 180.degree., and the wafer holder also moves the wafer in a way such that the contact point is moved on the turn table surface.