Althrough uniform B-spline has convexity-preserving property，the curve doesn't in terpolate any control points. If we insert two new contrl points between two cosecute coutrol points，the new points will merge the old points to form a new set of control points. we show that cubic B-spline curve generated by the new set of points interpolates all old control points，and the interpolating curve is convexity, preserving. The local modifications of the curve are possible. Finally，two numerical examples are given.