To prevent the frequent repetition of the acceleration and deceleration of driver's own vehicle even if a preceding vehicle frequently repeats the acceleration and deceleration during the following travel control for making the driver's own vehicle travel so as to follow the preceding vehicle.

During the following travel control (control of distance between two vehicles), whether or not the preceding vehicle frequently repeats the acceleration and deceleration is judged depending upon whether or not the number of times of the acceleration and deceleration of the preceding vehicle per a required period of time is more than a reference value. When it has been judged that the preceding vehicle is frequently repeating the acceleration and deceleration, the driver's own vehicle is controlled so as to keep the vehicle speed constant by switching-over the following travel control to the constant speed following control if the actual distance between two vehicles is within a dead zone determined so as to be in the range from (a target distance between two vehicles -α) to (the target distance between two vehicles +β). As a result, even if the preceding vehicle has frequently repeated the acceleration and deceleration, the frequent repetition of the acceleration and deceleration of the driver's own vehicle by following the preceding vehicle can be prevented. After that, when the actual distance between two vehicles has come out of the dead zone, the driver's own vehicle is controlled so as to keep the actual distance between two vehicles to be the target distance between two vehicles by returning the control to the ordinary control for the distance between two vehicles.