A target azimuth estimation algorithm of Synthetic Aperture Radar (SAR) images based on block sparse Bayesian learning was proposed. SAR images were highly sensitive to target azimuth, the SAR image with a special azimuth only highly correlate with those samples with approaching azimuths. The proposed method was developed based on the idea of sparse representation. First, all the training samples were sorted according to the azimuths to construct the global dictionary. Then, the sparse coefficients of test sample to be estimated over the global dictionary should be block sparse ones, that was the non-zero coefficients mainly accumulate in a local part on the global dictionary. The solved positions of the blocks effectively reflect the azimuthal information of the test sample. The block sparse Bayesian learning (BSBL) algorithm was employed to solve the block sparse coefficients and then the candidate blocks were chosen based on the minimum of the reconstruction errors. With the optimal block, the estimated azimuth was calculated by linearly fusing the azimuths of all the training samples in the block thus a robust estimation result could be achieved. The proposed method considered the azimuthal sensitivity of SAR images and comprehensively utilized the valid information in a local discretionary, so the instability of using a signal reference training sample could be avoided. Experiments were conducted on moving and stationary target acquisition and recognition (MSTAR) dataset to validate effectiveness of the proposed method while compared with several classical algorithms. The experimental results validate the superior performance of the proposed method.