By introducing curvilinear structures extraction (CSE) instead of watershed algorithm (WA) or nonmaximum suppression (NMS) to edge strength map (ESM), an improved ratio of exponentially weighted averages (ROEWA) edge detector with better capacity for weak edges detection is proposed to extract smooth edges and edge direction of synthetic aperture radar (SAR) images. Using the ROEWA, the ESM is calculated. Then the CSE algorithm is employed to extracted edges, by acquiring eigenvectors and eigenvalues of the Hessian matrix, the improved ESM (IESM) is obtained, which ensures the good weak edge detection capacity and smoothness of edges. Experimental results on simulated and real SAR images show that the improved ROEWA based on CSE attains better performance than the one using WA or NMS.