we proposes an improved alternating direction method of multipliers (ADMM) algorithm based on the relaxation technique and the prediction-correction framework, which introduces the new parameters in the subproblem x and the dual problem λ , so that the step size of each iteration is greater than 1, thereby improving the convergence of the algorithm. The convergence of the algorithm is proved in the framework of variational inequality. Moreover, the image deblurring problem in numerical experiments verifies that the algorithm is effective. Based on multiple sets of convergence criteria, the appropriate value is selected by comprehensively considering the rate of convergence and the quality of images.