A new scheme for constructing a Catmull-Clark subdivision surface with shape control is proposed, which interpolates the local vertices of a quadrilateral mesh with arbitrary topology. Firstly, utilizing the local property of the progressive iterative approximation method, this subdivision scheme chooses a subset of the vertices on the control mesh to be adjusted and remains the others unchanged in the iterative process, it results the limit surface of the subdivision interoplates the corresponding subset of the vertices on the initial mesh. Secondly, the shape control for Catmull-Clark subdivision in the proposed scheme is based on a two-phase subdivision. The two-phase scheme works by applying a modified Catmull-Clark subdivision for the initial mesh to generate a new mesh firstly, and then applying the regular Catmull-Clark subdivision for the new mesh to resulting the limit surface. The modified subdivision scheme carries a parameter for each face of the initial mesh, and these parameters provide the degrees of freedom for the shape control of the interpolating subdivision surface. It is proven that the scheme based on Catmull-Clark subdivision with shape control is convergent. The experimental examples are given to show that the method is effective both in local progressive interpolation and shape control.