A wire electrical discharge machine which performs electrical discharge machining on a workpiece by using electrical discharges generated by applying voltage across an electrode gap formed between a wire electrode and the workpiece, comprising: a first power circuit including a capacitor and configured to induce an electrical discharge by applying a first voltage across the electrode gap; a second power circuit configured to supply a machining current through the electrode gap by applying a second voltage across the electrode gap; and a gap voltage detector configured to detect the voltage across the electrode gap; characterized in that the wire electrical discharge machine further comprises a controller, wherein the controller includes: a first voltage control unit configured to apply the first voltage to the electrode gap in an intermittent manner by controlling the first power circuit; a discharge determiner configured to determine whether or not the electrode gap is in a discharging state during application of the first voltage, based on the detected voltage across the electrode gap; and a second voltage control unit configured to: when the electrode gap is determined to be in a discharging state, determine whether or not a machining current has been supplied to the electrode gap from the second power circuit after a previous application of a pulse of the first voltage, control the second power circuit to apply the second voltage to the electrode gap and supply the machining current when it is determined that no machining current has been supplied after the previous application of the pulse of the first voltage, and control the second power circuit to prohibit application of the second voltage to the electrode gap so as not to supply the machining current through the electrode gap when it is determined that the machining current has been supplied after the previous application of the pulse of the first voltage. a first power circuit including a capacitor and configured to induce an electrical discharge by applying a first voltage across the electrode gap; a second power circuit configured to supply a machining current through the electrode gap by applying a second voltage across the electrode gap; and a gap voltage detector configured to detect the voltage across the electrode gap; a first voltage control unit configured to apply the first voltage to the electrode gap in an intermittent manner by controlling the first power circuit; a discharge determiner configured to determine whether or not the electrode gap is in a discharging state during application of the first voltage, based on the detected voltage across the electrode gap; and a second voltage control unit configured to: when the electrode gap is determined to be in a discharging state, determine whether or not a machining current has been supplied to the electrode gap from the second power circuit after a previous application of a pulse of the first voltage, control the second power circuit to apply the second voltage to the electrode gap and supply the machining current when it is determined that no machining current has been supplied after the previous application of the pulse of the first voltage, and control the second power circuit to prohibit application of the second voltage to the electrode gap so as not to supply the machining current through the electrode gap when it is determined that the machining current has been supplied after the previous application of the pulse of the first voltage. when the electrode gap is determined to be in a discharging state, determine whether or not a machining current has been supplied to the electrode gap from the second power circuit after a previous application of a pulse of the first voltage, control the second power circuit to apply the second voltage to the electrode gap and supply the machining current when it is determined that no machining current has been supplied after the previous application of the pulse of the first voltage, and control the second power circuit to prohibit application of the second voltage to the electrode gap so as not to supply the machining current through the electrode gap when it is determined that the machining current has been supplied after the previous application of the pulse of the first voltage.