The ROEWA (Ratio Of Exponentially Weighted Averages) edge detector has been widely used in the extraction of the step edges in SAR images. The detector can only get the edge intensity, but it can not get the edge direction. A modified ROEWA edge detector is proposed to gain the edge direction with directional templates. After edge detection, a new edge selecting algorithm and a fast Hough transformation are proposed based on the edge direction, which can gain the straight lines in the images. The simulated result experiments the accuracy and the efficiency of the algorithm proposed, and the speckle noise is suppressed.