Abstract: The grey scale of the pixels in image is expressed by quantum bit and the relation between two pixels is described by means of the superposition of two quantum bit in this paper.Based on this，the average of linear hermitian operator in this superposition can be used for judging the edge of image and a new method for edge detection of image is so created.The rationality of the method is interpreted by probability theory here.A function of this new edge detecting method to compensate defect of human’s vision is proved theoretically and is verified in computer simulation.The edge caused by tiny change in grey scale of pixel in high or low grey scale area of image can be detected by using this method.