In an automatic follow-up control, a traveling control unit calculates and sets target intervehicular time on the basis of own vehicle velocity and calculates target acceleration on the basis of an intervehicular distance between an own vehicle and a preceding vehicle, preceding vehicle velocity, the own vehicle velocity, and the target intervehicular time to perform automatic brake control, automatic acceleration control, and the like. The target intervehicular time is calculated and set according to a function of the own vehicle velocity. The function is set as a function of a tendency that, as the own vehicle velocity increases, the target intervehicular time decreases. The function has at least a term in which a first set value and a second set value are defined in advance, the own vehicle velocity is raised to the power of the second value and then multiplied by the first set value.