1. A target tracking apparatus comprising: a target detecting device for detecting a target, which is to be tracked, within a detection area of a subject image represented by image data obtained by imaging a subject continuously; a detection area updating device, responsive to detection of the target by said target detecting device, for updating the detection area in such a manner that the detected target will occupy the center thereof; a motion detecting device, responsive to the target no longer being detected by said target detecting device, for detecting magnitude and direction of motion of the overall subject image in which the target is no longer detected; a detection area setting device for setting the detection area at a central portion of the subject image if the motion of the overall subject image detected by said motion detecting device is equal to or greater than a prescribed magnitude, and setting the detection area at an edge of the subject image in a direction opposite the direction of motion of the overall subject image, which has been detected by said motion detecting device, if the motion of the overall subject image detected by said motion detecting device is less than the prescribed magnitude; and a control device for controlling said target detecting device, said detection area updating device, said motion detecting device and said detection area setting device so as to repeat processing for detecting the target, processing for updating the detection area, processing for detecting the magnitude and direction of the motion, and processing for setting the detection area.