A wire electric discharge machine, which applies a high-frequency voltage to a machining gap between a wire electrode and a workpiece located at a predetermined distance from the wire electrode, thereby generating electric discharge to machine the workpiece, the wire electric discharge machine comprising: voltage application means configured to apply a bipolar voltage to the machining gap between the wire electrode and the workpiece for a period of one microsecond or less with a quiescent time longer than the duration of voltage application between each two adjacent cycles of voltage application provided; machining-gap voltage detection means for detecting a machining-gap voltage produced in the machining gap; duty cycle number counting means (7, 77) for counting the number of duty cycles of the voltage applied by the voltage application means for each unit time; open-circuit state identification means for identifying an open-circuit state where no electric discharge occurs after the voltage is applied, based on the machining-gap voltage detected by the machining-gap voltage detection means; open-circuit number counting means (7, 78) for counting the number of open-circuits identified by the open-circuit state identification means for each unit time; and a numerical controller adapted to obtain an average machining-gap voltage based on the number of duty cycles per unit time counted by the duty cycle number counting means (7, 77), the number of open-circuits per unit time counted by the open-circuit number counting means (7, 78), and a supply voltage or an average voltage for each duty cycle, wherein the open-circuit state identification means (7, 78) is configured to compare a full-wave-rectified machining-gap voltage waveform with a predetermined reference voltage within the quiescent time, to identify the open-circuit state if the reference voltage is exceeded, and to identify a closed-circuit state if the reference voltage is not reached, in contrast. voltage application means configured to apply a bipolar voltage to the machining gap between the wire electrode and the workpiece for a period of one microsecond or less with a quiescent time longer than the duration of voltage application between each two adjacent cycles of voltage application provided; machining-gap voltage detection means for detecting a machining-gap voltage produced in the machining gap; duty cycle number counting means (7, 77) for counting the number of duty cycles of the voltage applied by the voltage application means for each unit time; open-circuit state identification means for identifying an open-circuit state where no electric discharge occurs after the voltage is applied, based on the machining-gap voltage detected by the machining-gap voltage detection means; open-circuit number counting means (7, 78) for counting the number of open-circuits identified by the open-circuit state identification means for each unit time; and a numerical controller adapted to obtain an average machining-gap voltage based on the number of duty cycles per unit time counted by the duty cycle number counting means (7, 77), the number of open-circuits per unit time counted by the open-circuit number counting means (7, 78), and a supply voltage or an average voltage for each duty cycle, wherein the open-circuit state identification means (7, 78) is configured to compare a full-wave-rectified machining-gap voltage waveform with a predetermined reference voltage within the quiescent time, to identify the open-circuit state if the reference voltage is exceeded, and to identify a closed-circuit state if the reference voltage is not reached, in contrast.