An anisotropic diffusion filtering method is proposed to reduce multiplicative speckle noise in synthetic aperture radar images. A new anisotropic diffusion equation, which can effectively smooth speckles near the edges and reduce blocking artifacts in homogeneous regions, is established by embedding the mean curvature motion controlled by an adaptive coupling function into a traditional speckle reducing anisotropic diffusion equation. Moreover, a new direction-constrained diffusion function formed by combining the local directional ratios with the improved Frost filtering is introduced into the new anisotropic diffusion equation, so that it can further reduce blocking artifacts and obviously improve the edge distortion problem in the despeckled synthetic aperture radar images. Experimental results show that the proposed method can obviously reduce blocking artifacts, sufficiently smooth speckle noise in homogeneous regions and near the edges while preserving edges, and effectively improve the edge distortion problem. Visual quality and performance indexes of the despeckled images show that the proposed method outperforms several despeckling methods.