A method and apparatus for operating an electronic device is provided. The method includes transmitting, to a cover device, graphical data for displaying of the cover device, and detecting a user input on a display of the electronic device, wherein the displaying on the display of the cover device is interrupted based on the user input, wherein the cover device is capable of being folded, and wherein the cover device includes a first surface on which the display is located, and a second surface on which the electronic device is mounted.