Abstract: The necessary and sufficient conditions of G¹ continuity between two bicubic non-uniform B-spline surface patches are obtained，and the instinct conditions of the control vertices of the common boundary curve are presented．These conditions are directly represented by the control vertices of the two non-uniform B-spline patches．Meanwhile，some remarkable difference on the conditions of G¹ continuity between two adjacent Bézier patches in comparison with that between two adjacent non-uniform B-spline patches are studied．