A wire electrical discharge machine is provided with a rotating shaft for rotating a workpiece. In wire electrical discharge machining according to a machining program, a current average rotation radius at a current workpiece machining point is calculated for each predetermined period, based on average rotation radii at respective end points of a block to be executed and a directly preceding block and an amount of movement of the rotating shaft. Based on the calculated current average rotation radius, control is performed such that the speed of movement of the wire electrode relative to the workpiece machining point agrees with a command speed acquired from a machining power supply.