Abstract: In a cylinder grinding machine including grinder supporting table which rotatably supports a grinder for grinding a cylindrical workpiece, a mechanism for feeding the grinder supporting table toward the cylindrical workpiece and a device for relatively moving the workpiece and the grinder in their axial directions, there is provided a computer control apparatus. The control apparatus is constituted by a workpiece diameter measuring device, a central processing unit for calculating the diameter of the workpiece at respective positions along the axis of the workpiece and control means for controlling the amount of feed of the grinder supporting table such that diameter errors would be lesser than a permissible value.