A numerically controlled curved-surface machining unit equipped with three linearly moving axes and, at least, one rotary axis, including a simultaneous multiple-axis control NC machine numerically controlled by a numerical control unit with a numerical control NURBS interpolation function. The unit enables reading, as CL (cutter location) data, tool control point vector data and tool axis vector data, along a machining direction on a workpiece coordinate system for a curved surface, obtaining feed rates therefor, and calculation by conversion of the CL data into position vectors of three linear axes on a machine coordinate system, rotation angles and feed rates on the machine coordinate system so as to operate the simultaneous multiple-axis control NC machine on the basis of a machine configuration of the simultaneous multiple-axis control NC machine. The unit forms at least one NURBS curve having continuous curvature, calculates data therefor and converts the NURBS curve into NC data for NURBS interpolation.