An apparatus for processing a chamfering of an eyeglass lens, including means for inputting a width of the chamfering and a range of the chamfering from a periphery of a lens shape at at least one position adjacent to a nose or far away from the nose, arithmetic control means for obtaining a trace for the chamfering on a refractive surface of the eyeglass lens and obtaining the position of the edge end of the eyeglass lens after the processing of the chamfering, and means for displaying the trace of the chamfering by overlapping the lens shape.