A grinding machine is provided with first and second grinding wheels selectively used in dependence on the steps of machining operations. The second grinding wheel is grooved so that at least one oblique groove vertically crosses a contact surface on which a grinding surface of the second grinding wheel contacts with a workpiece, and thus, is capable of releasing a dynamic pressure in coolant generated between the grinding surface and the workpiece since coolant supplied from over the contact surface flows out from both of the upper and lower sides of the contact surface through the at least one oblique groove. Since it does not occur that fluctuations in the dynamic pressure generated in coolant cause the distance between the second grinding wheel and the workpiece to be varied, the accuracy in grinding the workpiece with the second grinding wheel can be enhanced.