Abstract: Interpolation to vertex positions and normals is one of important contents in parametric surface modeling. This paper presents an approach based on Catmull-Clark and Doo-Sabin subdivision schemes to generate the control net of bi-cubic B-spline surface interpolating the given vertices of initial net. The notion of stencils is introduced such that the normal interpolation is converted into the rotation transformation of stencils without influencing the effects of vertex interpolation, thus a C²-continuous surface interpolating given vertices and normals is obtained. Compared to traditional methods through stitching patches piece by piece, our method is more compact and has smoothness of higher degree. In addition, the method can be easily extended to high degree B-spline surfaces with arbitrary topology nets and it is also fairly useful for practical applications.