An elevator group control system includes a reference route generating portion, which for each elevator, generates a reference route which the elevator should follow with respect to the time axis and position axis; and an assignment portion which selects an elevator for assignment to a generated hall call so as to make the actual trajectory of each elevator closer to its reference route. Reference routes which guide the cage's trajectory into temporally equal interval condition are generated, and car assignment is executed to allow the cages to settle in temporally equal interval condition over a long period of time.