Based on the fourth-order anisotropic diffusion LLT model for image denoising, we have proposed a modified fixed point iterative algorithm. The proposed algorithm uses the steepest descent direction as the search direction in order to avoid computing directly the inverse matrices, thus reducing the roundoff error and improving the convergence rate. The convergence of the algorithm has been proved with the spectrum of matrix. Experiment results have illustrated that, for the “Lena” image which is corrupted with the noise of standard variance σ＝15, the signal to noise ratio (SNR) by our algorithm is improved greatly from SNR=11.208 8 to SNR=16.511 1 .