To enable a workpiece to be ground smooth, and grinding of the workiece to be carried out efficiently, without consideration of materials and properties, etc., of the workpiece and a grinding wheel.

A grinding wheel 9 rotated in fixed position, and a support table 10 capable of being displaced to the front and the rear and right and left f1, f2 by servomotors 14, 17 are provided, and a worktable 18 is mounted on this support table 10 so that it can be displaced within a certain distance through a guide track means 19 headed for the grinding wheel, while a work holding and rotating means 26 which rotates a work w by a servomotor 29 is provided on this worktable 18. Further, this machine is constructed by providing external force applying means 22, 25 to apply moving force for displacing the worktable toward the grinding wheel within the displacement extent by the guide track means 19, as well as by fitting a sensor 30 to detect the worktable being positioned at an end point of the grinding wheel side of the displacement extent by the guide track means 19.