An adaptive filter for smoothing images corrupted by signal dependent noise is presented. The filter is mainly developed for speckle suppression in medical B-scan ultrasonic imaging. The filter is based on mean filtering of the image using appropriately shaped and sized local kernels. Each filtering kernel, fitting to the local homogeneous region, is obtained through local statistics based region growing. Performance of the proposed scheme have been tested on a B-scan image of a standard tissue-mimicking ultrasound resolution phantom. The results indicate that the filter effectively reduces the speckle while preserving the resolvable details. The performance figures obtained through computer simulations on the phantom image are presented in a comparative way with some existing speckle iippression schemes.