The asymptotic curve is widely used in astronomy, mechanics, architecture and relevant subjects. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being boundary asymptotic curves of a surface and constructs the Bezier surface of bi-eleven degree interpolating the quintic Bezier asymptotic quadrilateral with given corner data. Some representative surfaces interpolating boundary as asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of the tensor-product Bezier surfaces is compatible with the CAD systems.