A 3D game machine includes a monitor for displaying images, a game control unit for controlling progress of a game, and an image control unit for generating and displaying a 3D image viewed from a viewing point of a simulated camera on a screen of the monitor. A transverse position and a height position of the head of a game player located in a play area before the screen of the monitor are detected using one ultrasonic transmitter and two ultrasonic receivers, and the viewing point of the simulated camera is so moved as to follow a displacing direction and a displacing amount of the detected position of the game player's head, thereby allowing the viewing point of the simulated camera to follow free movements of the game player so that images viewed from the viewing point intended by the game player are actively displayed.