Abstract At present, cad/cam (computer-aided design and manufacture) have fine wider and wider application in mechanical industry. For the complex surfaces, the traditional machine tool can no longer satisfy the requirement of such complex task. Only by the help of cad/cam can fulfill the requirement. The machining of the vane surface of the impeller leaf has been considered as the hardest challenge. Because of their complex shape, the 5-axis cnc machine tool is needed for the machining of such parts. The material is hard to cut, the requirement for the surface finish and clearance is very high, so that the manufacture quality of impeller leaf represent the level of 5-axis machining. This paper opened a new field in machining the complicated surface, based on a relatively more rigid mathematical basis. The theory presented here is relatively more systematical. Since the lack of theoretical guidance, in the former research, people have to try in machining many times. Such case will be changed. The movement of the cutter determined by this method is definite, and the residual is the smallest while the times of travel is the fewest. The criterion is simple and the calculation is easy.