An image display apparatus comprising: a display; an interface unit (130 or 135) configured to exchange data with a mobile terminal; a memory; and a controller configured to if there is a mirroring input, enter a mirroring mode; connect to the mobile terminal according to the mirroring mode; receive device information including a device ID, information of an application under execution, and an image of the application under execution from the mobile terminal during the mirroring mode between the image display apparatus and the mobile terminal; store the information of the application including an application ID, application version information and an application icon image in the memory; perform authentication of the mobile terminal based on the device information including the device ID, control the display to display an application execution image based on the image of the application from the mobile terminal during the mirroring mode; if the image of the application from the mobile terminal is not received any more, determine that the mirroring mode is terminated; after the mirroring mode is terminated, generate an execution icon of an application corresponding to the application execution image based on the stored application icon image; if there is an application list display input after generating the execution icon, control the display to display an application list including the generated execution icon; when a displayed execution icon of the application list is selected in a state in which the mirroring mode is terminated, transmit application information corresponding to the displayed execution icon of the application list to the mobile terminal for executing an application corresponding to the displayed execution icon of the application list in the mobile terminal so as to enter mirroring mode; and receive a second image of the application corresponding to the displayed execution icon of the application list executed in the mobile terminal through the interface unit and control the display to display a second application execution image based on the second image of the application received from the mobile terminal and corresponding to the displayed execution icon of the application list, wherein when an intensity of a wireless signal received from the mobile terminal is a designated intensity or more, the controller is configured to enter the mirroring mode and automatically display the application list including the generated execution icon. a display; an interface unit (130 or 135) configured to exchange data with a mobile terminal; a memory; and a controller configured to if there is a mirroring input, enter a mirroring mode; connect to the mobile terminal according to the mirroring mode; receive device information including a device ID, information of an application under execution, and an image of the application under execution from the mobile terminal during the mirroring mode between the image display apparatus and the mobile terminal; store the information of the application including an application ID, application version information and an application icon image in the memory; perform authentication of the mobile terminal based on the device information including the device ID, control the display to display an application execution image based on the image of the application from the mobile terminal during the mirroring mode; if the image of the application from the mobile terminal is not received any more, determine that the mirroring mode is terminated; after the mirroring mode is terminated, generate an execution icon of an application corresponding to the application execution image based on the stored application icon image; if there is an application list display input after generating the execution icon, control the display to display an application list including the generated execution icon; when a displayed execution icon of the application list is selected in a state in which the mirroring mode is terminated, transmit application information corresponding to the displayed execution icon of the application list to the mobile terminal for executing an application corresponding to the displayed execution icon of the application list in the mobile terminal so as to enter mirroring mode; and receive a second image of the application corresponding to the displayed execution icon of the application list executed in the mobile terminal through the interface unit and control the display to display a second application execution image based on the second image of the application received from the mobile terminal and corresponding to the displayed execution icon of the application list, wherein when an intensity of a wireless signal received from the mobile terminal is a designated intensity or more, the controller is configured to enter the mirroring mode and automatically display the application list including the generated execution icon.