A wire electric discharge machining apparatus according to embodiments includes a wire electrode, a wire supplying unit that supplies the wire electrode, a collecting motor that collects the wire electrode at a predetermined speed, a tension motor that controls a tension of the wire electrode between the wire supplying unit and the collecting motor, a speed calculating unit that calculates a traveling speed of the wire electrode at a predetermined time interval, a speed storing unit that stores the traveling speed calculated by the speed calculating unit, a differential speed calculating unit that calculates a differential speed between a current traveling speed output from the speed calculating unit and a past traveling speed stored in the speed storing unit, and a breakage detecting unit that detects breakage of the wire electrode by comparing the differential speed with a predetermined threshold.