PURPOSE: To grind a hourglass-barrel rotating workpiece accurately by grinding it with an abrasive wheel, whose turning shaft is vertical, being shiftable as rotating along a surface of the workpiece in all directions within a horizontal surface.

CONSTITUTION: An abrasive wheel 6, being vertical with a shaft center 13 of an hourglass workpiece 2, and having a tuning center 12 installed in a proper distance away from the shaft center 13 of the workpiece 2 is rotated by a rotative driving means 7. In addition, this abrasive wheel 6 is traveled along a surface of the workpiece 2 in all directions within the horizontal surface in relation to the shaft center 13 of the workpiece 2. With this constitution, a contact state between the workpiece 2 and the abrasive wheel 6 is always made constant, greatly improving the extent of abrasive finishing.