Abstract: Biorthogonal Catmull-Clark subdivision wavelet transforms constructed via lifting scheme have been proposed to speed up processing of geometric models. However, their compression qualities and noise-filtering effects are insufficient, particularly the model stability at low-resolution level is deficient. Therefore, a wavelet construction with progressive-interpolation-based biorthogonal Catmull-Clark subdivision is presented to generate a new control mesh whose limit surface progressively interpolates all vertices in the original quadrilateral mesh with arbitrary topology. It can achieve an exponential convergence rate and slight differences of subdivision surfaces between successive levels, which are suitable to data compression, noise-filtering, and so on. Combined with the local and in-place lifting operations, the proposed wavelet transform can dramatically decrease the memory consumption and computation complexity. Experimental results show that compared with the previous biorthogonal Catmull-Clark wavelet constructions, the proposed wavelet transform achieves high compression ratio, steady noise-filtering and better progressive transmission quality, decreasing the bits/vertex of 3D meshes about 14%, improving the PSNR of reconstruction model about 5%, and reducing the time costs of coding and decoding by 6% and 9%, respectively.