Three-axis CNC surface machining entails a series of processes including rough cutting, intermediate cutting and finish cutting for a reference surface defined in CAD/CAM. This study is targeting development of an integrated NURBS surface interpolator that can incorporate rough, intermediate and finish cutting processes. In each process, volume to be removed and cutting condition are different according to the shape of a part to be machined and the reference surface. Accordingly, the proposed NURBS surface interpolator controls motion in real-time optimized for the machining conditions of each process. In this paper, a newly defined set of G-codes is proposed such that NURBS surface machining through CNC is feasible with minimal information on the surface composition. To verify the usefulness of the proposed interpolator, through computer simulations on NURBS surface machining, total machining time, size of required NC data and cutting force variations are compared with the existing method.