An elevator group control system is provided which stably keeps cage's position in temporally equal interval condition over a long period of time. The present invention provides a system comprising: reference route generating means, which for each elevator, generates a reference route which the elevator should follow with respect to the time axis and position axis; and assignment means 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. Since reference routes which guides the cage's trajectory into temporally equal interval condition are generated and car assignment is executed so as to make the respective cages follow their reference routes, it is possible to allow the cages to settle in temporally equal interval condition over a long period of time.