1. A method of processing an image of an electronic device, the method comprising: identifying, by a controller of the electronic device, edge components of a background image by a unit of a predetermined size; identifying, by the controller, input coordinate points of a touch input which is input on a touch screen; determining, by the controller, distorted coordinate points by applying the edge components to the input coordinate points; and displaying, by the controller, a drawing image which is formed by connecting the distorted coordinate points on the background image, wherein the determining of the distorted coordinate points by applying the edge components to the input coordinate points comprises moving the input coordinate points to horizontal and vertical coordinates corresponding to the edge components, by calculating the horizontal and vertical coordinates for the input coordinate points, wherein the identifying of the edge components comprises detecting a value of the vertical edge component and a value of the horizontal edge component by a predetermined unit, and wherein the moving of the input coordinate points to the horizontal and vertical coordinates corresponding to the edge components comprises: moving the input coordinate points vertically in proportion with the magnitude of the value of the vertical edge component, and moving the input coordinate points horizontally in proportion with the magnitude of the value of the horizontal edge component.