An ATM switching system which includes PVC allocation circuits corresponding to output queues. At the time of arrival of the leading cell of each burst data, if the output line has room, the PVC of the burst data is stored as information for admission and identification. The subsequently-arriving cells having the same PVC identification information as the stored identification information are input to an output buffer, and the cells of the remaining burst data are all discarded. Even when a plurality of burst data compete for the same output line, the fact that all the cells other than the first-arriving admitted burst data are discarded prevents the cells from being input other than within a predetermined bandwidth and localizes the burst data affected by the cell discarding due to output queue overflow.