Edge detection is the focus and difficult point for speckle reduction anisotropic diffusion. Traditional methods typically rely on the estimation of mean and variance in edge detection. The precision of the estimations influences the accuracy of edge detection. In this paper, we present an anisotropic diffusion filter based on image entropy. This method uses image entropy as an edge detector to eliminate the error due to the estimation of mean and variance, and improves the edge detection capability. The experimental results show that the visual quality and evaluation indexes of the new method outperform those of the traditional methods.