1. A handwriting input method of an electronic device using a touch pen, the handwriting input method comprising: displaying an execution screen of an application on a touch screen in response to the application being executed; overlapping a handwriting input layer, which is configured for a handwriting input, with the execution screen; inputting a handwriting image on an area of the handwriting input layer using the touch pen; determining a data type of the input handwriting image as a text or an image based on an attribute of an area of the execution screen, overlapping with the area of the handwriting input layer in which the handwriting input image has been input, and recognizing the input handwriting image as the determined data type; and applying a recognized result of the determined data type to the application, wherein the recognizing comprises: converting the input handwriting image into the text and recognizing the converted text, in response to determining the data type of the input handwriting image as the text, and recognizing an image corresponding to the input handwriting image, without text conversion, in response to determining the data type of the input handwriting image as the image.