A collision determination device determines the possibility of collision between a host vehicle and the other object on the basis of a shortest arrival time calculated by a shortest arrival time calculation unit and a passage time at each point of the host vehicle acquired by a vehicle route candidate acquisition unit. In this way, even if a locus to be taken by the other object is not generated, the shortest arrival time at which the other object can arrive at each point of the route candidate of the host vehicle with a predetermined first displacement is calculated, thereby determining the possibility of collision between the host vehicle and the other object. Therefore, it is possible to reduce a computational load for determining collision and to accurately determine collision between the host vehicle and the other object.