Commonly, surface/surface intersect algorithm is repeatedly used to solve the offset surface/surface intersections. It doesn't make full use of similarity of intersect curve topology to simple offset surface/surface intersection problem. The algorithm presented in this paper pre-processes two parametric surfaces to achieve points, called topology transition points, which produce an effect on intersect curve structure, number and location. According to topology transition points distribution graph, initial point search strategy and intersect curve topology can be fixed. The algorithm is tested, and can be proved to overcome the degenerate conditions such as loop leaking, singularity leaking and can calculate the initial point effectively.