A workpiece centering apparatus 1 is provided on a lathe having a spindle 33, an independent chuck 34, and upper and lower tool rests 37, 41, and has sandwiching members 11, 12 mounted to the tool rests 37, 41, respectively, and capable of contacting the outer peripheral surface of a workpiece W, and a centering control section 15 for moving the tool rests 37, 41 and thereby moving the sandwiching members 11, 12 to their respective centering positions which are the positions of the sandwiching members 11, 12 when the center position of a portion to be machined of the workpiece W coincides with the axis of the spindle 33 in a state where the portion to be machined of the workpiece W is being sandwiched and held by the sandwiching members 11, 12, and then causing the independent chuck 34 to grip the workpiece W.