In modern society the image processing has been applied to various digital devices such as smartphone, digital camera, and digital TV. In the field of image processing the edge detection is one of the important parts in the image processing procedure. The image edge means point that the pixel value is changed between background and object rapidly, and includes the important information such as magnitude, location, and orientation. The performance of the existing edge detection method is insufficient for the image degraded by AWGN(additive white Gaussian noise) because it detects edges by using small weighted masks. Therefore, in this paper, to detect edge in AWGN environment effectively, we proposed an algorithm that detects edge as calculated gradient of sorting vector which is transformed by estimated mask from new pixel according to each region.