Speckle noise contaminates medical ultrasound images, and the suppression of speckle noise is helpful for image interpretation. Traditional ultrasound denoising (i.e., despeckling) methods are developed on two-dimensional static images. However, one of the advantages of ultrasonography is its nature of dynamic imaging. A method for dynamic ultrasound despeckling is expected to incorporate both the spatial and temporal information in successive images of dynamic ultrasound and thus yield better denoising performance. Here we regard a dynamic ultrasound video as three-dimensional (3-D) images with two dimensions in the spatial domain and one in the temporal domain, and we propose a despeckling algorithm for dynamic ultrasound named the 3-D Gabor-based anisotropic diffusion (GAD-3D). The GAD-3D expands the classic two-dimensional Gabor-based anisotropic diffusion (GAD) into 3-D domain. First, we proposed a robust 3-D Gabor-based edge detector by capturing the edge with 3-D Gabor transformation. Then we embed this novel detector into the partial differential equation of GAD to guide the 3-D diffusion process. In the simulation experiment, when the noise variance is as high as 0.14, the GAD-3D improves the Pratt's figure of merit, mean structural similarity index and peak signal-to-noise ratio by 24.32%, 10.98%, and 6.51%, respectively, compared with the best values of seven other methods. Experimental results on clinical dynamic ultrasonography suggest that the GAD-3D outperforms the other seven methods in noise reduction and detail preservation. The GAD-3D is effective for dynamic ultrasound despeckling and may be potentially valuable for disease assessment in dynamic medical ultrasonography.