A centering apparatus that centers a cylindrical workpiece set on a rotary table, comprising a position detection probe that is movable in a direction orthogonal to the rotation axis of the rotary table, and is adapted to come into contact with the workpiece and a position detection block; and a centering controller that controls centering of the workpiece through control of the position detection probe, wherein the centering controller comprises: workpiece peripheral face position measuring means for bringing the position detection probe into contact with at least three points of the peripheral face of the workpiece, which are offset circumferentially from each other, and measuring each contact position between the position detection probe and the workpiece, with rotation of the rotary table stopped; runout calculating means for calculating an amount of runout of an axis of the workpiece and a largest runout phase position that is a phase position of the workpiece, at which the runout amount is largest, based on the measured contact positions; characterized by a centering shaft member that is movable in a direction orthogonal to a rotation axis of the rotary table; a workpiece contact that is provided at the centering shaft member, and is adapted to come into contact with, as the centering shaft member moves, a peripheral face of the workpiece and push the workpiece in a radial direction of the workpiece; and the position detection block is provided at the centering shaft member; wherein the centering controller controls centering of the workpiece also through control of the centering shaft member, and the centering controller also comprises: block position measuring means for bringing the position detection probe into contact with the position detection block and measuring a position of the position detection block; phase position indexing means for turning the rotary table so as to set the largest runout phase position of the workpiece in a position opposed to the workpiece contact; relative position deriving means for deriving relative positions of the workpiece and the workpiece contact in a state where the largest runout phase position of the workpiece is in the position opposed to the workpiece contact as a result of turning of the rotary table, based on the contact positions measured by the workpiece peripheral face position measuring means and the position of the position detection block measured by the block position measuring means; and pushing means for, after the phase position indexing means sets the largest runout phase position of the workpiece in the position opposed to the workpiece contact, centering the workpiece by moving the centering shaft member based on the relative positions of the workpiece and the workpiece contact such that the workpiece contact pushes the workpiece by a distance corresponding to the runout amount. workpiece peripheral face position measuring means for bringing the position detection probe into contact with at least three points of the peripheral face of the workpiece, which are offset circumferentially from each other, and measuring each contact position between the position detection probe and the workpiece, with rotation of the rotary table stopped; runout calculating means for calculating an amount of runout of an axis of the workpiece and a largest runout phase position that is a phase position of the workpiece, at which the runout amount is largest, based on the measured contact positions; block position measuring means for bringing the position detection probe into contact with the position detection block and measuring a position of the position detection block; phase position indexing means for turning the rotary table so as to set the largest runout phase position of the workpiece in a position opposed to the workpiece contact; relative position deriving means for deriving relative positions of the workpiece and the workpiece contact in a state where the largest runout phase position of the workpiece is in the position opposed to the workpiece contact as a result of turning of the rotary table, based on the contact positions measured by the workpiece peripheral face position measuring means and the position of the position detection block measured by the block position measuring means; and pushing means for, after the phase position indexing means sets the largest runout phase position of the workpiece in the position opposed to the workpiece contact, centering the workpiece by moving the centering shaft member based on the relative positions of the workpiece and the workpiece contact such that the workpiece contact pushes the workpiece by a distance corresponding to the runout amount.