A driving support apparatus installed in a host vehicle calculates an overlap ratio relating to a target object positioned ahead of the host vehicle within the same traffic lane, as the ratio of the width of the target object to its lateral distance from a lane marker line of the traffic lane, and also detects the motion condition of the object (i.e., stationary, moving towards, or in the same direction as the host vehicle, or moving laterally with respect to the forward direction of the host vehicle). An amount of compensation for retarding or advancing the commencement of a collision avoidance operation by the driving support apparatus is determined based on the overlap ratio and/or the motion condition of the target object.