A call admission control system in an asynchronous transfer mode exchange includes a unit for describing attribute parameters of a cell from the subscriber terminal; a unit for calculating, based on the attribute parameters, the average and the dispersion of the traffic speeds of the call; a unit for managing data of the average and the dispersion on each output route and data relating to each subscriber; and a unit for calculating the total average and the total dispersion of the data speeds on the selection output route; and a unit for calculating prediction values of cell abandon rate and end-to-end delay based on the average and the dispersion on the selected output route calculated by the total average and dispersion calculating unit, and for comparing the prediction values with the required service quality of cell discard rate and end-to end delay, for determining whether or not the requesting call may be connected.