Abstract: The directional projection problem of B-spline surfaces can be solved by computing the roots of a non-linear equation system．Usually one or none of the roots of the equation system is mapping to the closest point where the minimum distance occurs, aand most of the computation on finding the roots of the equation system is unnecessary．A simple but efficient geometric pruning method is presented for the directional projection problem of B-spline surfaces．It utilizes the convex property of the B-spline basis functions and the robust subdivision algorithm of B-spline surface, aand it is able to directly detect whether the minimum directional distance occurs at a corner point or at a boundary curve of the B-spline surface．Compared with conventional root-finding methods of a nonlinear equation system, ait can exclude most of the roots and needs no numerical iterative method such as the Newton method．The proposed algorithm can be applied in the intersection testing problem between a plane and a B-spline surface, aand the encapsulation box computation problem of B-spline surfaces．Examples are given to show both efficiency and robustness of the new method．