Edge enhancement of noisy ultrasound images is important for medical diagnosis. Conventional edge enhancement methods are mainly directed to emphasizing the high-frequency components of the image. Because these methods emphasize also the noise of image, they are not suitable for noisy ultrasound images with speckle noise. In this paper, we propose an edge enhancement method using mathematical morphology based on a geometrical characteristics of the image, using locally variable structuring elements. We show that the proposed method enhances the edge of ultrasound images without noise emphasis.