The speckle reduction is an important problem in coherent imaging, such as synthetic aperture radar or ultrasound imagery. Speckle is a nonadditive and nonwhite process, and the reduction of speckle without blurring sharp features is known to be difficult. We present a new speckle reduction algorithm that utilizes an anisotropic directional filter that adapts to the proximity and direction of nearest important features. To remove speckle without blurring important features, the locations and direction of edges in the image are estimated. Then for each pixel in the image, the distance and angle to the nearest edge are computed by an efficient algorithm and stored in distance and angle maps. Finally, for each pixel, an anisotropic directional filter aligned to the nearest edge is applied. The shape and the orientation of the filter are determined from the distance and the angle maps. The new speckle reduction algorithm is tested with both synthesized and real synthetic aperture radar images. The performance of the new algorithm is also compared to those of earlier speckle reduction approaches. We show that the new algorithm performs favorably compared to other speckle reduction algorithms in reducing speckle without blurring important features.