To provide a grinding machine and a centering method for the centers thereof in which the requisite space for the center support rotating mechanism for a workpiece and the in-feed mechanism is reduced to facilitate miniaturization and in which it is easy to secure the space for the supply and discharge of the workpiece and sizing measurement. A motor built-in type main spindle retaining a rotary drive center and a motor built-in type tailstock spindle retaining a tailstock center are swiveled by in-feed means eccentrically supporting them, whereby the rotary drive center and the tailstock center make an in-feed motion with respect to a grinding wheel.