A compound regularized multiple sparse bayesian learning algorithm for sparse unmixing is presented, in which sparse bayesian learning model is integrated in the linear hyperspectral pixel unmixing. On the framework of sparse Bayesian Learning model based on MMV (Multiple Measurement Vectors), the parameters in the model is established with the probability, and a L2,1 norm regularization-based multiple sparse bayesian learning model for spectral unmixing is constructed by bayesian inference, taking the non-negativity and sum-to-one property of abundances into the convex objective function. The compound regularization problem is decomposed into several single regularization problems solving by a variable separation method, and the regularization parameters of the model are updated by an adaptive adjustment algorithm. Experimental results on both synthetic and real hyperspectral data demonstrate that the proposed method outperforms the greedy algorithms and the convex algorithms with a better spectral unmixing accuracy, and is suitable for complex combination of endmembers and low signal-to-noise ratio hyperspectral data.