In carrying out electric discharge machining of a graphite or carbon-composite workpiece by a wire electric discharge machine, a voltage lower than that used in machining a metal workpiece by the wire electric discharge machine is supplied to a machining gap. Further, the peak value and the pulse width of a total discharge current flowing from a power supply device for electric discharge machining to a wire electrode are adjusted within ranges of 30 to 150 amperes and 0.3 to 6.4 microseconds, respectively.