Disclosed is a chamfering machine which enables a smooth cutting operation by allowing a workpiece to be fixed to a position corresponding to an optimal cutting condition. The chamfering machine comprises a cutting position groove, which is formed in the bottom surface of an upper guide, and into which a part of the outer circumferential surface of a workpiece is inserted, wherein the central part of the cutting position groove is formed to correspond to the cutting end of a chamfering cutter. The machining method is configured such that the chamfering cutter enters perpendicular to a centerline direction of a circular material and, after entering while cutting, to a point where the cutting end of a cutting tip is in line with the centerline, rotates a tubular material or revolves the chamfering cutter around the tubular material and thus can cut the surface of the circular material.