A wire electrical discharge machining apparatus includes a target-control-section calculating unit calculating a target control section, which is indicated by a start point and an end point of the corner control in a current electrical discharge machining during the finish machining, based on a machining parameter; an actual-control-section calculating unit correcting the start point and the end point of the corner control, which are indicated in the target control section calculated by the target-control-section calculating unit, and calculating an actual control section, based on a magnitude of a shape error of the corner portion in a previous electrical discharge machining during the finish machining; and a speed controlling unit controlling the feed speed of the wire such that an amount of machining per unit time in the actual control section becomes equal to that when a portion other than the corner portion is machined.