A wire electrical discharge machine for performing electrical discharge machining on a workpiece to be machined by applying voltage to an electrode gap formed between a wire electrode and the workpiece to generate electrical discharge at the electrode gap under predetermined machining conditions while conveying the wire electrode along a transfer path, includes: a wire breakage detector for detecting a breakage of the wire electrode; a position calculator for calculating the breakage position of the wire electrode in the transfer path; and an adjustment unit for adjusting the machining conditions when the breakage position is in a predetermined section of the transfer path.