Image deblurring is one of the classical problems in image processing. The main purpose of image deblurring is to restore the images corrupted by blur and additive noise while preserving edges and details. We focus on the nonblind image deblurring (NBID) problem. In order to obtain good deblurred images, we propose an NBID method based on a compound regularization model associated with the shearlet-based sparsity and the weighted anisotropic total variation. Based on this model, we present an alternative iterative scheme which consists of the operator splitting and penalty techniques. The split Bregman-based multivariable minimization iteration is introduced to optimize the proposed NBID inverse problem. Compared with some previous methods, the experiments demonstrate the efficiency and viability of the proposed method for preserving sharp edges and structural details of the image while mitigating the artifacts.