1. An apparatus for displaying a three-dimensional (3D) image, the apparatus comprising: a display device displaying alternately the left eye image and the right eye image; and a system generating image information regarding a left eye image and a right eye image and generating a synchronization signal for the left eye image and the right eye image to display alternately the left eye image and the right eye image on the display device, the system including: an image input unit receiving images to be displayed on the display device; an image discriminating unit for discriminating the left eye image or the right eye image from the images inputted from the image input unit by calculating a luminance value of a current image, detecting a peak value based on the calculated luminance value, position-comparing the detected peak value with a stored peak value of a previous frame, and determining the left eye image or the right eye image based on a result of the position-comparing; and a synchronization signal generating unit generating a synchronization signal according to the discrimination result from the image discriminating unit to supply the generated synchronization signal to shutter glasses and the display device to synchronize the shutter glasses and the display device.