A wire electrical discharge machining apparatus includes an NC control device, and the NC control device determines, during taper machining, whether the type of machining is a type (first type) in which an upper die is located on a workpiece side in comparison with a lower die or a type (second type) in which the upper die is located on the side opposite to the workpiece in comparison with the lower die on the basis of a machining program and corrects the positional relationship between the upper die and the lower die in accordance with the determined type of machining.