A wire electrical discharge machine includes: a voltage application unit for repeatedly applying a voltage to an electrode gap between the workpiece and the wire electrode at a predetermined cycle; a switching element connected in parallel with the electrode gap and configured to short-circuit the electrode gap; and a control section for controlling the switching element so as to short-circuit the electrode gap in a pause period during which the voltage is not applied. The control section adjusts a short-circuiting period in which the electrode gap is short-circuited according to the machining shape specified by a machining program.