An elevator group control apparatus collectively controls an elevator system where at least two cars can travel in each shaft independently of each other. The apparatus has a destination floor registration device installed at each hall for passengers to register destination floors and to indicate to passengers which cars will serve respectively for the registered destination floors. Priority zones and a shared zone for upper cars and for lower cars are set; a judgment is made as to whether the shared zone set can be entered by an upper or lower car; a car is put on standby based on the judgment a car is sent to a withdrawal floors, as necessary, after a service is completed. A car is selected as a candidate for assignment to a destination call if, according to the destination to be served by each car and the zones set for each car, so that the car would cause neither collision nor safety stop; and a car is assigned based on the selection.