Classic nonlinear filter does well for suppressing impulse noise and edge preserving. However, classic nonlinear filtering is not good at reducing the mixture of Gaussian noise and impulse noise. In this paper, we investigate nonlinear filtering techniques to eliminate the mixture of impulse noise and Gaussian noise. Based on fuzzy theory, we present a weighted average filter by making use of the fuzzy membership functions to optimize the weights of the filter. Computational results, which have been obtained from experiments for noise attenuation, indicate that the new algorithm is promising.