Dictionary learning methods have been extensively used in different types of image andsignal processing tasks. In a number of applications, the collected data/signal may havea multi-subspace structure and be perturbed with outliers. These motivate the use ofrobust and block-sparse signal representations. In this paper, a new algorithm for learn-ing a block-structured dictionary in the presence of outliers is proposed. It is based on α−divergence and has the advantage of tolerating the presence of outliers. A block co-ordinate descent approach is adopted to obtain simple closed-form solutions for both thesparse coding and dictionary update stages. Finally, experimental results illustrating thesuperiority of the proposed method over some state-of-the-art dictionary learning meth-ods, are provided.