A wire electric discharge machine for machining a workpiece into a desired shape by changing a relative position between a wire electrode and the workpiece while causing discharge by applying a voltage to a machining gap between the wire electrode and the workpiece, the wire electric discharge machine comprising: a secondary power supply including a DC power supply and a switching element (23, 24, 25, 26), wherein the secondary power supply is configured to apply an AC pulse voltage; a primary power supply including a DC power supply, a switching element (28, 29, 30; 28, 29, 30, 35, 36), and a discharge capacitor, wherein the discharge capacitor and the DC power supply are configured to be connected with each other and to be disconnected; a voltage detection unit disposed between the wire electrode and the workpiece; and a numerical controller, the numerical controller comprising a storage unit storing, in advance, a voltage value assumed when a dielectric breakdown occurs between the wire electrode and the workpiece; and a comparison unit configured to compare a detected voltage value with the voltage value stored in the storage unit, wherein, the numerical controller is configured to, as a result of comparison by the comparison unit, when the detected voltage value is smaller than the voltage value stored in the storage unit, determine that a dielectric breakdown has occurred between the wire electrode and the workpiece, characterized in that the numerical controller is further configured to initiate supply of a pulse current using the discharge capacitor of the primary power supply when it is determined that the dielectric breakdown has occurred. a secondary power supply including a DC power supply and a switching element (23, 24, 25, 26), wherein the secondary power supply is configured to apply an AC pulse voltage; a primary power supply including a DC power supply, a switching element (28, 29, 30; 28, 29, 30, 35, 36), and a discharge capacitor, wherein the discharge capacitor and the DC power supply are configured to be connected with each other and to be disconnected; a voltage detection unit disposed between the wire electrode and the workpiece; and a numerical controller, the numerical controller comprising a storage unit storing, in advance, a voltage value assumed when a dielectric breakdown occurs between the wire electrode and the workpiece; and a comparison unit configured to compare a detected voltage value with the voltage value stored in the storage unit, wherein, a storage unit storing, in advance, a voltage value assumed when a dielectric breakdown occurs between the wire electrode and the workpiece; and a comparison unit configured to compare a detected voltage value with the voltage value stored in the storage unit, wherein, the numerical controller is configured to, as a result of comparison by the comparison unit, when the detected voltage value is smaller than the voltage value stored in the storage unit, determine that a dielectric breakdown has occurred between the wire electrode and the workpiece, characterized in that the numerical controller is further configured to initiate supply of a pulse current using the discharge capacitor of the primary power supply when it is determined that the dielectric breakdown has occurred.