In a wire electrical discharge machining apparatus, an upper main-discharge power supply is connected between an upper conducting terminal and a workpiece using an upper main-feeder line capable of configuring outward and homeward paths, and a lower main-discharge power supply is connected between a lower conducting terminal and the workpiece using a lower main-feeder line capable of configuring outward and homeward paths. Moreover, a sub-discharge power supply is connected between the upper conducting terminal and the workpiece and between the lower conducting terminal and the workpiece using an upper and a lower sub-feeder lines that have higher impedances than the impedances of the upper and the lower main-feeder lines and can configure outward and homeward paths.