In a numerical control grinding machine, movements of a wheel head and a work table respectively in first and second directions perpendicular to each other are controlled by reference to first and second present position registers which respectively represent positions of cylindrical and shoulder grinding surfaces of a grinding wheel rotatably carried on the work head A reference member is secured to the work table, and a wheel head reference point is defined on the wheel head. A memory device stores data which represents positions in the first and second directions, of the wheel head reference point relative to a workpiece rotational axis and the reference member when the wheel head and the work table are at respective original positions. The memory device further stores data which represents positions in the first and second directions, of the cylindrical and shoulder grinding surfaces relative to the wheel head reference point. When given a command after the present position registers lose their contents due to power failure or emergency stop, a central processing unit of a numerical controller for the machine calculates the present positions of the cylindrical and shoulder grinding surfaces based upon the stored data in the memory device and sets the present position registers respectively with the calculated present positions.