In this paper, we consider the output contention problem with the objective of increasing the throughput for asynchronous fransfer mode (ATM) switching systems with delay-sensitive traffic. We propose a cell scheduling algorithm to increase the throughput of a switching system. The maximum throughput is increased by up to 0.949. The efficiency, (output trunk utilization)/(input trunk utilization), is almost equal to 100%, and it is independent of the switch size and the traffic load. The cell scheduling algorithm is also shown to be able to provide high throughput not only for delay-sensitive traffic but also for traffic which can tolerate longer queueing delay. The mean cell waiting time of delay-sensitive traffic is reduced. That is, delay-sensitive traffic is transmitted as soon as possible. In previous works, the switching network usually has consisted of a sorting network followed by a routing network. However, in the switching system implemented with our cell scheduling algorith, it is sufficient for a sorting network to establish input/output paths through it simultaneously without conflicts, and it is not necessary to append a routing network to a sorting network. With our cell scheduling algorithm, it is impossible for any out-of -sequence cells to be received by the destinations on an input/output path. This, in turn, leads to the design of simpler protocols for the synchronization of real-time services such as voice and video communications. Consequently, our algorithm may offer an effective alternative for an ATM switching system.