Finding the solution of single measurement vector (SMV) problem with an unknown block-sparsity structure is considered. Here, we propose a sparse Bayesian learning (SBL) algorithm simplified via the approximate message passing (AMP) framework. In order to encourage the block-sparsity structure, we incorporate a parameter called Sigma-Delta as a measure of clumpiness in the supports of the solution. Using the AMP framework reduces the computational load of the proposed SBL algorithm and as a result makes it faster. Furthermore, in terms of the mean-squared error between the true and the reconstructed solution, the algorithm demonstrates an encouraging improvement compared to the other algorithms.