PURPOSE: To enable the machining of high roundness and shorten workpiece supply/discharge time taken up in a machining cycle so as to heighten machining efficiency in a centerless grinding machine for grinding workpieces in the state of holding each workpiece supported on each support plate between a grinding wheel and a regulating wheel.

CONSTITUTION: There is provided an index drum 18 with plural support plates B disposed at equal spaces apart around a regulating wheel 17. This index drum 18 is partially rotated by a partial drive unit and stopped after positioning the support plates B in turn into a machining position. A grinding wheel 5 is cutting-fed to a workpiece W on the support plate B in the machining position.