The problem of finding sparse solutions to underdetermined systems of linear equations arises in several real-world problems (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe an efficient block active set coordinate descent algorithm that at each iteration use a bunch of variables (i.e. those variables which are non-active and violate the most some specific optimality conditions) to improve the objective function. We further analyze the convergence properties of the proposed method. Finally, we report some numerical results showing the effectiveness of the approach.