An offset distance of an obstacle from a traveling-path center line of a vehicle at the time the obstacle is detected is calculated, and then this offset distance of the obstacle from the traveling-path center line of the vehicle is corrected based on a turning radius of the traveling vehicle detected at the time a specified period of time has lapsed. Thereby, even in a case where the vehicle travels on a road with a curve that changes a radius of curvature of the traveling-path center line (turning radius of the traveling vehicle) quickly during the specified period of traveling time, the above-described offset distance can be properly corrected based on an updated turning radius of the traveling vehicle. Thus, a relative position of the obstacle with respect to the vehicle can be predicted accurately.