In this paper, we apply a fixed point method to solve the total variation-based image denoising problem. An algebraic multigrid method is used to solve the corresponding linear equations. Krylov subspace acceleration is adopted to improve convergence in the fixed point iteration. A good initial guess for this outer iteration at finest grid is obtained by combining fixed point iteration and geometric multigrid interpolation successively from the coarsest grid to the finest grid. Numerical experiments demonstrate that this method is efficient and robust even for images with large noise-to-signal ratios.