This paper proposes a novel method for image denoising based on the maximum entropy principle. For an image corrupted by Gaussian and impulse noise, impulse noise with high value is detected first using rank statistics, and then removed by a local Gaussian filter. To remove the noise left, an improved self-adaptive non-local filter, with the weights obtained based on the maximum entropy principle, is performed. The experimental results demonstrate that our approach has significant ability to remove any mix of Gaussian and impulse noise in terms of quantitatively image evaluation and qualitatively visual effect.