For SAR images, traditional edge detection methods can hardly extract edges taking account of noise suppression, the integrity of edges and the veracity of edge position. However, Wedgelet, which is a multiscale geometric analysis tool, has an advantage of catching linear features. Aiming at further reducing speckle noise on SAR images, we modified the cost function of wedgelet transform. Besides, proper transform scales is selected in order to highly fasten the transform without affecting the quality of approximation. Based on the improved Wedgelet transform, edge detection is preformed. Experimental results show that the proposed method can suppress speckle noise on SAR images successfully and extract edges from SAR images effectively.