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