In this paper, we focus on deblurring and denoising problems for blurred images with moderate or large noise. A new algorithm for the discretized system is presented.Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems of equations. We adopt the Krylov subspace method to accelerate the outer nonlinear iteration. Numerical experiments demonstrate that this method is efficient and robust even for images with large noise-to-signal ratios and signal to blurring quantity ratios.