In image deblurring problems, both local and nonlocal regularization priors are well studied. Local regularization prior assumes piecewise smoothness and transform-based sparsity, while the nonlocal one exploits self-similarity of images. We proposed a mixed regularization model which incorporates the advantages of both local adaptive sparsity prior and nonlocal sparsity prior resulting from the nonlocal self-similarity, and thus encourages a solution to simultaneously express both the local and nonlocal natures of images. The deblurring problem with mixed regularization can be transformed into a constrained optimization problem with separable structure via the variable splitting. Then this constrained optimization problem is solved by the alternating direction method of multipliers. Experimental results with a set of images under varying conditions demonstrate that the proposed method achieves the state-of-the-art deblurring performance.