A driving support ECU performs an inter-vehicle-distance control and a following-travel steering control. When an inter-vehicle-distance target vehicle and a following-travel steering target vehicle are the same specific other vehicle as each other, and there is a potential cutting-in vehicle between an own vehicle and the specific other vehicle, the driving support ECU newly specifies the potential cutting-in vehicle as the inter-vehicle-distance target vehicle at a first time point in a cutting-in period and newly specifies the potential cutting-in vehicle as the following-travel steering target vehicle at a second time point in the cutting-in period.