During the ultrasonic medical image edge detection, one of the difficult problems is that there am some speckles that show strongly variance of image gray level, the speckles reduce the space difference and remain the detailed structure under cover.Edge detection algorithms have had fairly limited application in ultrasound imaging. High levels of speckling present in ultrasound images make accurate edge detections difficult. In this paper, a novel edge detection method based on mathematical morphology is presented. Firstly, according to the statistical characteristic of the speckle, the speckle filtering method based on multidirectional morphological structure is presented. The experiment shows that the speckle noise has been filtered and image details have been preserved by the method based on local statistical property of the image, the edge detection result shows that this method is reliable and effective. Certainly the speckle filtering and the edge detection are not the final objective and would like to be proved and perfected in the further research of ultrasonic image analyzing.