A Expressing method of the edge of image region is important in the studing and applying of image. It will influence the veracity of expressing and recognizing of region. A free curve of created method which discussed by the author have been used to approach the edge of image region. Since the free curve pass through the given points and need not converse compute, the speed of creating curve is very quickly. Also the curve are smoothness and fairness, the curve is close to edge of image region. The experiment presents the efficiency of the method.