Abstract: In this paper, based on some property in digital image and the theory on the application of partial differential equations in image processing, we take the pixel values of an image as the temperature of some plane object. By applying the theory of partial differential equations and the theory of image zooming in image processing, we derive a mathematical model based on a new type of initial and boundary value problem for heat equations for image zooming. We also design a difference scheme for experiments. Our experimental results show that the model works well on the image zooming and reaches better quality of zoomed image.