The authors describe an efficient and fast algorithm for finding the minimum distance between two convex polyhedrons in three-dimensional space. To obtain the minimal distance, the proposed computational scheme is based on a direct approach to minimize the distance function which produces a succession of optimal search directions along the boundary of the objects. This algorithm combines the gradient projection method (Rosen, 1960) and an additional optimal search direction when the gradient projection method leads to a zigzagging phenomenon. In this case, the additional optimal search direction accelerates significantly the convergence of the process. Extensive numerical experiments with convex polyhedra showed the performance of the algorithm when compared with previous approaches.>