Sparse unmixing of hyperspectral images aims to separate the endmembers and estimate the abundances of mixed pixels. This approach is the essential step for many applications involving hyperspectral images. The multiscale spatial sparse hyperspectral unmixing algorithm (MUA) could achieve higher accuracy than many state-of-the-art algorithms. The regularization parameters, whose combinations markedly influence the unmixing accuracy, are determined by manually searching in the broad parameter space, leading to time consuming. To settle this issue, the adaptive multi-scale spatial sparse hyperspectral unmixing algorithm (AMUA) is proposed. Firstly, the MUA model is converted into a new version by using of a maximum a posteriori (MAP) system. Secondly, the theories indicating that andnorms are equivalent to Laplacian and multivariate Gaussian functions, respectively, are applied to explore the strong connections among the regularization parameters, estimated abundances and estimated noise variances. Finally, the connections are applied to update the regularization parameters adaptively in the optimization process of unmixing. Experimental results on both simulated data and real hyperspectral images show that the AMUA can substantially improve the unmixing efficiency at the cost of negligible accuracy. And a series of sensitive experiments were undertook to verify the robustness of the AMUA algorithm.