Generating subdivision surfaces with complicated curve interpolation constrains is a concerned topic for computer graphics and geometric modeling. In this paper an efficient method that can interpolate cubic NURBS curves is proposed for generating the subdivision surfaces. A 憇ymmetric zonal mesh?is constructed by designing symmetric quadrilaterals for both sides of the control polygon of the interpolated curve. Applying the non-uniform Catmull-Clark subdivision scheme proposed by Sederberg et al. to the symmetric zonal mesh, it is proved that the mesh can converge to the interpolated curve. As a result, the limit surface of the polygonal mesh containing the symmetric zonal meshes is the subdivision surface satisfying the curve interpolation constrains. This algorithm can interpolate both the single NURBS curve and the curve mesh consisting of several NURBS curves. Therefore it can be widely used for product shape design and graphic software development.