A grinding method by a multifunction grinding machine, the multifunction grinding machine having; a supporting device supporting a workpiece which includes on its outer peripheral surface a curved concave surface having a radius of curvature R1; a multifunction wheel slide moveably mounted relative to said supporting device and having a rough grinding wheel having a radius R2 and a finish grinding wheel having a radius R3 said rough grinding wheel and said finish grinding wheel being selectively used; and a controller configured to control the grinding of said workpiece by a grinding wheel, one of said rough grinding wheel and said finish grinding wheel is selected as the grinding wheel; the grinding method by said multifunction grinding machine, comprising; executing a rough grinding process grinding said workpiece supported by said supporting device by said rough grinding wheel until only a pre-set remaining amount to be removed in the consecutive finish grinding process is left on the workpiece; and executing a finish grinding process grinding said remaining amount to be removed by finish grinding of said workpiece by said finish grinding wheel after said rough grinding process, wherein the workpiece is continuously supported by said supporting device; characterized in that each of a radius R2 of said rough grinding wheel and a radius R3 of said finish grinding wheel is formed to be smaller than said radius R1 of curvature of said curved concave surface of the workpiece, said pre-set remaining amount to be removed during finish grinding is set based on at least one of thermal displacement of said multifunction grinding machine and changing amount of grinding force based on said rough grinding wheel; said pre-set remaining amount to be removed during finish grinding is the same amount at the portion of the curved concave surface of the workpiece and the remaining portion excluding the curved concave surface. a supporting device supporting a workpiece which includes on its outer peripheral surface a curved concave surface having a radius of curvature R1; a multifunction wheel slide moveably mounted relative to said supporting device and having a rough grinding wheel having a radius R2 and a finish grinding wheel having a radius R3 said rough grinding wheel and said finish grinding wheel being selectively used; and a controller configured to control the grinding of said workpiece by a grinding wheel, one of said rough grinding wheel and said finish grinding wheel is selected as the grinding wheel; the grinding method by said multifunction grinding machine, comprising; executing a rough grinding process grinding said workpiece supported by said supporting device by said rough grinding wheel until only a pre-set remaining amount to be removed in the consecutive finish grinding process is left on the workpiece; and executing a finish grinding process grinding said remaining amount to be removed by finish grinding of said workpiece by said finish grinding wheel after said rough grinding process, wherein the workpiece is continuously supported by said supporting device; characterized in that each of a radius R2 of said rough grinding wheel and a radius R3 of said finish grinding wheel is formed to be smaller than said radius R1 of curvature of said curved concave surface of the workpiece, said pre-set remaining amount to be removed during finish grinding is set based on at least one of thermal displacement of said multifunction grinding machine and changing amount of grinding force based on said rough grinding wheel; said pre-set remaining amount to be removed during finish grinding is the same amount at the portion of the curved concave surface of the workpiece and the remaining portion excluding the curved concave surface.