A combination grinding machine grinds a plurality of axially arranged portions of a workpiece by use of a grinding wheel supported rotatably on a first wheel head and a superfinishing wheel supported rotatably on a second wheel head. A numerical control unit controls feed units for the first and second wheel heads in order to move the first and second wheel heads independently of each other in the axial direction of the workpiece and in the direction perpendicular to the axial direction, such that each of the axially arranged portions is ground by the grinding wheel, and simultaneously with this, another ground portion is superfinished by the superfinishing wheel.