Abstract: In a computerized numerical controller for a grinding machine, various grinding modes in which a plurality of portions on a cylindrical workpiece are respectively ground and plural sets of machining data each for use in machining a corresponding one of the workpiece portions are input by a manual data input device for storage in a memory device under the control of a data processor. For preparation of an NC program for the workpiece, the data processor first decides a grinding order in which the workpiece portions are successively ground, based upon the grinding modes and the machining data stored in the memory device. The grinding order is decided in accordance with a predetermined rule designed to decrease the number of dressing operations effected on a grinding wheel of the grinding machine. Then, the data processor automatically prepares a NC program based upon the decided grinding order and the machining data.