Disclosed is a display control apparatus and method in a mobile terminal capable of outputting video data to an external display device, which implements a function of using other services in the mobile terminal, separately from the service provided to the external display device connected with the mobile terminal. To accomplish the above function, the controller determines whether an event occurs or not during displaying video data sent by the mobile terminal on the external display device and upon occurrence of an event, displays a screen for processing the event on the mobile terminal. Thus, a user can enjoy concurrent service by using other services through the mobile terminal while continuing to watch video data currently being displayed on the external display device. In addition, irrespective of the screen of the external display device, information relative to the event is only displayed on the mobile terminal so that a user's privacy can be fully protected.