In this paper, we present an O(n²) algorithm for finding the exact shortest paths from a fixed source point to all  other points on a triangulated polyhedral surface of a convex polytope in three-dimensional space using the concept of funnels   on the surface. Our algorithm  builds the sequence tree  by recursively splitting funnels. Because of special shape of these funnels (their left boundaries are straightest geodesics), funnels are determined explicitly   and do not rely on  unfolding technique. Number of operations in our algorithm is relatively small comparing with the number of operations in Chen and Han's algorithm, 1990.