In a target detection apparatus mounted in a vehicle, a target detector is configured to detect a target present in a forward direction of the vehicle based on image information acquired from an imager to capture images of a scene ahead of the vehicle. A position-of-collision calculator is configured to calculate an expected position of collision at which the target is expected to collide with the vehicle in the future based on a position of the target relative to the vehicle. A first determiner is configured to, based on the expected position of collision calculated by the position-of-collision calculator, determine whether or not a situation exists where a determination as to whether or not the target is a traversing target that is a target moving in a direction transverse to a forward direction of the vehicle can be made based on an optical flow of the target.