An elevator group supervisory control system for selecting the most suitable car among a plurality of elevators, when a hall call is made, to assign to the hall call, comprising: temporary assigning means for temporarily assigning the car by a conventional method such as a fuzzy group supervisory control based on group data representing states of the elevator system at the moment when a new hall call is made; and a neural net for receiving numerical values converted from group data including the result of judgment of the temporary assigning means and outputting an assignment fitness of each elevator. It decides the most suitable elevator from the output pattern of the neural net to assign to the hall call.