When an own vehicle makes a follow-up traveling control targeting a preceding vehicle traveling ahead of the own vehicle, in case where the widthwise movement of the preceding is detected and a second preceding vehicle traveling ahead of the preceding vehicle is detected, the preceding vehicle is regarded as undertaking to pass the second preceding vehicle and acceleration of the own vehicle is inhibited. Further, in a situation where the preceding vehicle and the second preceding vehicle run in parallel, these vehicles can be recognized discriminatingly from each other based on the memorized widths of theses vehicle and the direction of the widthwise movement of the preceding vehicle. Further, when it is judged that the preceding vehicle travels faster than the second preceding vehicle, the target of the follow-up traveling control is changed to the second preceding vehicle.