An apparatus for calibrating the centering of polishing heads in a polishing machine that is equipped with a plurality of spindles onto which polishing heads are mounted and a method for using such apparatus are disclosed. In the apparatus, a calibration disc is provided which has a hollow shaft mounted at a center of the bottom surface of the disc. A centering pin slidingly engaging an elongated cavity in the hollow shaft such that its protruded tip portion may be adjusted by using a locking device such as a set screw for different calibration procedures. The present invention novel apparatus can be used to calibrate the positioning of a polishing head mounted in a spindle with a pedestal in a load cup that is equipped with a center alignment aperture. The calibration can be conducted not only in the X, Y direction (or in the circumferential direction) of the spindle movement, but also in the Z direction (or a sweep direction) of the traversing spindle that occurs during a polishing operation.