PURPOSE: To perform machining continuously from rough grinding to finish grinding thus to perform curved face grinding accurately and efficiently by mounting a plurality of grinding wheels having different composition onto single shaft then moving said shaft in axial direction.

CONSTITUTION: First grinding wheel 2a is positioned by means of a stopper 12a and an air-cylinder 13 to perform rough grinding of curved face on a work 5. Thereafter, second grinding wheel 2b is moved through the operation of a stopper 12b and the air-cylinder 13 until contacting against the work 5 to perform finish grinding of curved face on the work 5. Then third grinding wheel 2c is moved to the position contacting against the work 5 to perform finish grinding of the curved face on the work 5. During this process, it is not required to remove the grinding wheel, to rebalance the grinding wheel or to perform dressing.