Abstract: A wire discharge machine includes a wire electrode arranged with a gap from a workpiece, and a constant-voltage power supply that applies a high-frequency voltage between the workpiece and the wire electrode, and generates discharge between the workpiece and the wire electrode by applying the high-frequency voltage to machine the workpiece. The wire discharge machine further includes a current measurement unit that measures a current value of a current flowing from the constant-voltage power supply, a determination unit that determines a state between electrodes, which is a state between the workpiece and the wire electrode, based on a combination of a result of a threshold determination of the measured current value and a result of a threshold determination of a change value in the current value, and a control unit that controls a gap between the workpiece and the wire electrode based on the determined state between electrodes.