A vehicle-installation intersection judgment apparatus determines whether a target object such as a pedestrian is located ahead and to one side of the vehicle, and if so, judges whether the object is moving laterally to intersect with the advancement of the vehicle. Successive amounts of lateral displacement of the object are periodically derived, each amount is compared with a displacement threshold, a count is made of the number of times that the displacement threshold is exceeded, and the count is compared with a predetermined count threshold. The judgment concerning the target object is made based upon whether the count threshold is attained.