Current medical ultrasound imaging suffers from grainy type speckles, which highly degrade the image details and hence reduce the diagnosis information contained in the images. Various filtering techniques for speckle reduction were previously proposed, including the standard median and Wiener filters. However, their performances are still limited in the sense that either speckles are not fully suppressed or edges and point features are not well preserved. In this paper, we first discuss about the statistical Nakagami distribution and analytical multiplicative noise models of speckles in ultrasound images, and then we propose an adaptive filter, named as Nakagami multiplicative adaptive filter (NaMAF), based on these models for effective speckle reduction and feature preservation. Performances of the proposed adaptive filter are compared with that of standard speckle reduction filters, showing that the proposed NaMAF performs best in terms of best visual effect and largest signal-to-noise ratio (SNR) when tested on phantom and in vivo images and least mean-square error (MSE) when tested on simulated images.