A workpiece support apparatus is provided with a plurality of support members. The support members support a workpiece. Each support member moves along a moving path to a machining position while the support member is held at a first holding position for supporting the workpiece or a second holding position which is spaced apart from the first holding position. At least one support member is displaced from the first holding position to the second holding position or from the second holding position to the first holding position along a machining trajectory, before the support member arrives at the machining position whenever each support member is moved to the machining position.