To restrain delay of deceleration timing of an own vehicle to prevent a sense of incongruity when a preceding vehicle is transferred to a deceleration state, by setting and maintaining inter-vehicle distance between it and the detected preceding vehicle to a target inter vehicle distance, and by providing a correcting means for limiting own vehicle's acceleration to the estimated or detected acceleration of the preceding vehicle.

A controller 20 for running control, by controlling a brake/ control device 8, an engine power control device 9, a transmission control device 10, based on inter-vehicle distance L detected by an inter-vehicle distance sensor 12, wheel speeds VwL, VwR detected by wheel speed sensors 13L, 13R, and output signals of a front and back acceleration sensor 14, performs following- running control for following-running a car with maintaining an adequate inter- vehicle distance between it and a preceding vehicle. In addition, when the preceding vehicle goes into an acceleration state during the following-running control, by setting the detected or estimated acceleration of the proceeding vehicle as an acceleration upper limit of an own vehicle, generation of unnecessary acceleration state when the proceeding vehicle goes into an deceleration state is certainly prevented.