To improve riding comfort by suppressing change of increase and decrease of deceleration to the utmost and not giving discomfort to a driver etc. when decelerating and stopping his or her own vehicle based on stop detection of preceding vehicle, and moreover not to generate unnecessary change of deceleration to the utmost.

This control unit calculates repeatedly the distance from the preceding vehicle at an expected stop position based on the present deceleration of own vehicle 1 as the estimated stop distance between the two vehicles by a stop distance calculation means, determines repeatedly whether the estimated stop distance between the two vehicles is within tolerance from prescribed near limit stop distance between the two vehicles near the preceding vehicle to prescribed far limit stop distance between the two vehicles by a determination means. When it is determined to be within tolerance, the own vehicle 1 is decelerated while maintaining the own vehicle 1 at present deceleration speed. When it is determined out of tolerance, the own vehicle 1 is decelerated by the new deceleration speed by calculating new deceleration speed by which estimated stop distance between two vehicles falls in the tolerance, and controls the own vehicle 1 to stop following by suppressing change of increase and decrease of deceleration to the utmost.