 the relative traveling speed is controlled so that it can be a speed not lower than the faster speed of the two traveling speeds. The present invention provides a wire electric discharge machine in which electric discharge energy is supplied between a wire electrode and a workpiece by a machining electric power supply means so as to machine the workpiece in gas when the wire electrode and the workpiece are relatively traveled with each other by a positioning means, comprising a control means for controlling the positioning means so that a relative traveling speed of the wire electrode with the workpiece can be set at a constant speed not lower than a predetermined speed at which a short circuit between the electrodes can not continue for a predetermined period of time 