The present invention is intended to provide a technique which is capable of detecting a collision position of a moving object crossing a road and a subject vehicle with a higher degree of accuracy. In the present invention, in cases where the moving object crossing the road into which the subject vehicle has entered is detected at the time when the subject vehicle has turned to the right or to the left, the direction of a moving vector of the moving object is fixed to a direction which is set based on a shape of the road into which the subject vehicle has turned to the right or to the left. Then, the collision position of the moving object and the subject vehicle is predicted based on this moving vector of which the direction is fixed.