A saddle curve is formed by intersection of two tubes. The trajectory control of saddle curve is usually carried out through approximating the curve as segments of straight line/circular arc for CNC interpolation. Based on the principle of space analytic geometry, this paper proposes a new trajectory control approach to directly interpolate the saddle curve for automated welding/cutting system. Simulation of the direct interpolation algorithm of saddle curve has been carried out to verify the effectiveness of the proposed algorithm. It also demonstrates that the interpolation error is well within the accuracy requirements and the proposed algorithm is potentially useful for the cutting/welding of saddle curve of tubular joints.