This paper presents a new technology, which is the normal tracing, for NC point-grinding of the curve. The development of the technology is based on the simultaneous three-axis machining. By controlling the superposition between the rotary surface of the grinding wheel and the normal vector of the curve, point contact between them is realized. So grinding just like turning, the abrasive machining of the complex curve is easy to be realized. The main advantage of the technology is the fact that it can not only reduce the deformation of the grinding wheel and simplify the NC programming, but also improve surface quality and profile accuracy. This paper builds the mathematic model of the normal tracing by analyzing the geometric property and the kinematic relationship between the wheel and the work piece. Then the control algorithm of the normal tracing is given and used in a new-type digital curve grinder successfully, MD9040 developed by ourselves.