A wire electrical discharge machine includes an upper wire guide and a lower wire guide supporting a wire electrode, a probe provided on an upper guide block having the upper wire guide, an offset storage unit for storing an offset amount from the upper wire guide to the probe, a position shift drive unit for changing the relative position between the table, and the upper and lower wire guides, a drive controller for controlling the position shift drive unit, a contact position calculator for calculating a contact position that is a position of the probe when it comes in contact, and a machining start position calculator for calculating a machining start position of the wire electrode, based on at least two contact positions and the offset amount. The drive controller controls the position shift drive unit so that the position of the wire electrode becomes the machining start position.