Anisotropic diffusion has good effect on reducing noise and preserving edge, but it may lose some details due to the blocky effect and can not suppress speckle effectively. The Laplacian factor is used to process the observed image which is considered as a piecewise planar image, so the Fourth Order Anisotropic Diffusion (FOAD) can avoid the blocky effect. The edge is preserved and enhanced by the Line Edge Detector (LED) based on stick technique and hypothesis test optimizing method. An approach called the Fourth Order Anisotropic Diffusion and Edge Enhancing (FOADEE), where the LED is combined with the FOAD, is presented. For quantitative evaluation and comparison with the LED, the FOAD and the FOADEE, two parameters as measure of the noise suppression and edge preservation are introduced. It is proved that the novel method can not only suppress speckle prominently but also preserve even enhance edge and useful details effectively by applying it to the phantoms and tissue images.