This paper presents an efficient and accurate direct interpolation algorithm for saddle curve formed by intersection of two tubes, an important manufacturing problem in automated welding/cutting field. The algorithm is able to directly interpolate the saddle curve with non-Cartesian configuration. Simulation of the saddle curve interpolation algorithm has been carried out on the Matlab platform. The results demonstrate that interpolation error is well within the accuracy requirements of typical machining. It also shows that the trajectory control program based on the algorithm can work with high efficiency.