A surface of a workpiece, from which the burr is removed, is traced when a machining tool is pressed onto the surface of the workpiece under force control so as to find the positional data of the surface shape (S1). This positional data is corrected by an error caused by a bend of a robot (S2). The thus obtained positional data is compared with the target shape of the surface, from which the burr is removed, obtained from CAD data (S6, S10). A shift of the surface shape in the normal line direction is found (S7, S11). The burr generation start position, the burr generation end position and the height of the burr are found by the shift start position (S8), the shift end position and the shift size (S14). A machining program is made which is composed of a pass connecting the burr end position with the burr start position and also composed of a cutting pass for removing the burr, and the thus made machining program is executed (S16, S17). As the burr position is found and the burr is removed when the machining tool is moved to the burr position, the burr can be effectively removed. Due to the foregoing, it is possible to provide a finishing machine characterized in that useless burr removing actions can be reduced and, further, that the overcutting of a workpiece can be prevented.