1. A method or following a detected moving object using a video camera having panning, tilting and zooming functions, comprising the steps of: a) storing succeeding and preceding frames produced by said camera into first and second memories respectively and controlling the panning, tilting and zooming functions of said video camera according to a position and a size of said moving object; b) performing a motion compensation on said preceding frame to compensate for a motion of a background image of said moving object so that coordinates of said preceding frame are transformed to coordinates of the succeeding frame; c) detecting an image difference between the motion-compensated preceding frame and said succeeding frame and determining from the image difference a position and a size of the moving object; and d) repeating the steps (a) to (c) by using said position and said size of the step (c) when the step (b) is repeated.