PURPOSE: To put a uniform edge on a cutter having fine deformation and recesses and projections in a lengthwise direction.

CONSTITUTION: A slidable body 28 is installed slidably freely on a base stage 15 capable of reciprocating in a lengthwise direction of a cutter 1, and a rotary grinding wheel 36 to grind the cutter 1 is set up in the slidable body 28 through a slidable member 30, and a grinding quantity setting device 37 to set an extension quantity of the rotary grinding wheel 36 is arranged between the slidable member 30 and the base stage 15, and copy grinding is carried out on the cutter 1 by means of an edge superfinishing device where a fluid pressure cylinder 39 to push-press the slidable member 30 to the cutter side is installed in the slidable body 28.