Abstract: In a numerical control grinding machine using a grinding wheel made of cubic boron nitride, a computerized numerical controller controls the infeed movement of a wheel head to effect a rough grinding and a first fine grinding on a rotating cylindrical workpiece by the grinding wheel and to halt the first fine grinding in response to a sizing signal from a sizing device which measures the diameter of the workpiece being ground. At the halt of the first fine grinding, the numerical controller advances rest jaws to press the workpiece upon the grinding wheel until another sizing signal is issued from the sizing device. Until the number of the workpieces ground after each truing operation reaches a predetermined number, the numerical controller increase the infeed rate of the grinding wheel in each of the rough and first fine grindings toward a desired infeed rate on a step-by-step basis.