Abstract: This paper presents a robust algorithm for the computation of the intersection of an implicit surface and a parametric surface. Analytic representation of intersection as a plane algebraic curve is obtained, and then numerical techniques are used to compute characteristic initial points (border points, turning points and singular points).Monotonic intersection segments are traced in three-dimensional space. So it is easy to tackle with the step and the tolerance. The algorithm has been proved to be reliable, efficient and accurate.