Abstract: Interpolating an arbitrary topology mesh by a smooth surface plays important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing Catmull-Clark surface that interpolates a given mesh. The control mesh of the interpolating surface is obtained by one Catmull-Clark subdivision of the given mesh with modified geometric rule. Two methods-push-back operation based method and normal-based method-are presented for the new geometric rule. The interpolation method has the following features: (1) Efficiency: we obtain a generalized cubic B-spline surface to interpolate any given mesh in a robust and simple manner. (2) Simplicity: we use only simple geometric rule to construct control mesh for the interpolating subdivision surface. (3) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (4) Freedom: for each edge and face, there is one degree of freedom to adjust the shape of the limit surface. These features make interpolation using Catmull-Clark surfaces very simple and thus make the method itself suitable for interactive free-form shape design.