In ultrasound (US), optical coherence tomography, synthetic aperture radar, and other coherent imaging systems, images are corrupted by multiplicative speckle noise that obscures image interpretation. An anisotropic diffusion (AD) method based on the Gabor transform, named Gabor-based anisotropic diffusion (GAD), is presented to suppress speckle in medical ultrasonography. First, an edge detector using the Gabor transform is proposed to capture directionality of tissue edges and discriminate edges from noise. Then the edge detector is embedded into the partial differential equation of AD to guide the diffusion process and iteratively denoise images. To enhance GAD's adaptability, parameters controlling diffusion are determined from a fully formed speckle region that is automatically detected. We evaluate the GAD on synthetic US images simulated with three models and clinical images acquired in vivo. Compared with seven existing speckle reduction methods, the GAD is superior to other methods in terms of noise reduction and detail preservation.