We propose an algorithm to recover the latent image from the blurred and compressed input. In recent years, although many image deblurring algorithms have been proposed, most of the previous methods do not consider the compression effect in blurry images. Actually, it is unavoidable in practice that most of the real-world images are compressed. This compression will introduce a typical kind of noise, blocking artifacts, which do not meet the Gaussian distribution assumed in most existing algorithms. Without properly handling this non-Gaussian noise, the recovered image will suffer severe artifacts. Inspired by the statistic property of compression error, we model the non-Gaussian noise as hyper-Laplacian distribution. Based on this model, an efficient nonblind image deblurring algorithm based on variable splitting technique is proposed to solve the resulting nonconvex minimization problem. Finally, we also address an effective blind image deblurring algorithm which can deal with the compressed and blurred images efficiently. Extensive experiments compared with state-of-the-art nonblind and blind deblurring methods demonstrate the effectiveness of the proposed method.