When a preceding vehicle moves away during follow-up running control, it is determined whether or not a forward obstacle is recognized. When a forward obstacle is recognized, it is determined whether or not the forward obstacle satisfies any of obstacle specifying conditions corresponding to a plurality of preset types. A basic threshold value set corresponding to the satisfied type is corrected by three correction values so as to set first to third estimated-collision-time determining values. The estimated-collision-time determining values are compared with an estimated collision time of a subject vehicle with respect to the forward obstacle, and acceleration control on the subject vehicle is limited stepwise in accordance with the comparison values.