Abstract: In recent years, some wavelets constructed via local lifting have been proposed to accelerate the compression of geometric models. Unlike the traditional wavelet-based compression with global optimisation, their compression ratios are still not sufficient, particularly at low-bit rates. In this paper, we present a novel efficient wavelet-based compression approach using the matrix-valued Loop subdivision on triangular meshes. Based on the local lifting scheme, the computation of the wavelet transform is highly efficient and requires low memory usage. With the shape controls introduced by the matrix-valued subdivision, our approach can greatly improve the fitting quality of surfaces while keeping the efficient data compression. The experimental results showed that our wavelet transform had better performance on balancing the efficiency and compression ratios.