The paper studies effective ways to sharpen images by using of partial differential equation and the classical image sharpening operators. Based on the physical meaning of heat equation, by regarding the gray values of an image as the temperature on a flat object, a model on anti-heat equation is obtained. Under the assumptions of the blurred image is the result of the original image filtered by the heat equation and the time t is small enough, we establish a model for image sharpening, which is solved by means of Sobel operator. The results of numerical experiments show that the method can make the image sharper and obtain clearer image. Sharpened image hasn’t moved information, at the same time noise doesn’t appear, it does keep the edges and details in the original image. The algorithm maintains stably over a long time, that is, the sharpened image does not been blurred again with the increase of the number of iterations.