To lengthen the service life of a grinding wheel in spherical or nonspherical surface machining and to improve machining quality.

A wheel spindle stock 20 is fitted to a Y-axis saddle 30 through a turning device 32 so as to be able to elevate the stock 20 in a Y-direction and to turn it around a turning axis Q pointing in an X-direction. The outer peripheral surface of a grinding wheel 22 is formed in a curved surface with the radius of curvature (r) (constant). A contact part between the grinding wheel 22 and a workpiece W is continuously changed by changing the turning angle of the wheel spindle stock 20. The Y-axis saddle 30 is vertically moved in conformity to the change of the turning angle of the wheel spindle stock 20 to perform machining in the state of a contact point between the workpiece W and the grinding wheel 22 being always positioned on a workpiece spindle 11 from the X-direction view.