A new CNC lathe driven by a linear motor has been developed to realize the machining of complex non-axisymmetric curved surfaces with rotational axis such as eccentric and spiral cylindrical volume, conical cams and artificial femoral stem. These have been realized by milling and/or grinding machines. In this case, there is a serious problem. It takes a long time to machine by milling or grinding. Furthermore, the machining point between a curved surface and a milling tool or a grinding wheel can be regarded as a single point contact just as same as lathe turning. We propose a new turning method that improves the productivity remarkably by using a driven rotary tool with its unique tool layout. In this report, the machining result of the curved surface by the proposed turning method and the feasibility are also reported.