Aiming at the problem of local curvature interference in tool path generation of five-axis CNC machining of complex free-form surface, this paper attempts to apply the theory of differential geometry to tool path generation. Based on the tangent plane at the Cutter Contacting point(CC point), the maximum principal curvature and minimum principal curvature of the tool surface at the CC point were calculated, and the normal curvature model in any direction on the tool surface was established. Similarly, for the workpiece surface, the normal curvature model in any direction on the workpiece surface was established by using the theory of maximum principal direction in differential geometry. According to the above two normal curvature mathematical models, the distance between adjacent cutting... positions and the distance between adjacent tool paths were calculated and deduced. At the same time, the mathematical expression to avoid local curvature interference was given to modify the tool attitude angle. The example results show that the proposed method has good effect in avoiding local curvature interference and reducing the total length of tool path. It can provide a theoretical basis for improving machining accuracy and efficiency in the field of complex surface precision machining.