Blind image restoration aims to accurately estimate the blur kernel and the wanted clear image with no-reference. Existing researches show that the use of the Total Variation to model the high-order image gradient prior constraints can effectively suppress the blocking artifact generated in the restored image. On the basis of experimental observation and research, this paper proposes to use the sparse prior constraint model to regularize the blind restoration process to obtain a better image restoration performance. Our method makes use of the sparsity of the high-order gradient of the image and combines it with the low-order gradient to construct the mixed gradient regularization term. At the same time, an adaptive factor based on image entropy is introduced to adjust the ratio of the two types of gradient priors in the iterative optimization process so as to obtain better convergence. Simulated and experimental results prove that compared with the existing state-of-the-art methods of blind image restoration, the proposed method has superior image restoration performance.