Abstract: To overcome the artifacts and incomplete filtering in the denoising process of SAR images, a SAR despeckling algorithm where the sparse structure meets Gaussian Scale Mixture (GSM) model is proposed. The mathematic model derivation of the algorithm is based on Bayes principle and the statistical property of speckle noise. We use the probability rather than the Euclidean distance to measure the weight in the block matching process; by utilizing the structural similarities of the image blocks, we can classify the homogeneous region and heterogeneous area efficiently and get a better mean estimated value of the block. Also, the PCA dictionary learning method is used to train the sub-dictionary of each image patch, which achieves the Simultaneous Sparse Coding (SSC) process. The model is solved via iteration and regularization, and a local optimized solution of the denoised image matrix is obtained. The algorithm is verified with both simulated SAR images and real SAR images, and the experimental results demonstrate that the proposed approach can improve ENL effectively, and has a competitive performance in terms of despeckling and the protection of local structural characteristics and textural features, when compared with the state-of-the-art despeckling algorithm.