[Problem] To machine a workpiece such as a hard brittle material or difficult-to-cut material innovatively and accurately and to improve the machining rate significantly.[Solution Means] In grinding a workpiece W by a cup grinding wheel 3 while supplying a slurry 5 containing abrasive grains, the grinding wheel 3 is rotated at low peripheral speed. No more than 500 m/min., preferably 30 to 430 m/min., is appropriate for the peripheral speed of the grinding wheel 3. The slurry 5 at a flow rate of no more than 4.0 ml/cm2/h, preferably of 1.0 to 2.0 ml/cm2/h is dropped or sprayed little by little onto a ground surface of the workpiece W.