The various services that a broadband integrated services digital network (B-ISDN) carries, have a wide range of delay, delay jitter and cell loss probability requirements. Design of appropriate control schemes for B-ISDN is an extremely important and challenging problem. In this paper, we proposed multiplexing algorithm with both delay and loss priorities in order to satisfy the diverse requirements. For the implementation of cell lose priority, we assumed that voice cells are generated as non-discardable(i.e., high priority) and discardable (i.e., low priotity)cells. The low priority voice cell may be discarded inside the network if congestion occurs. The cell dropping scheme is shown to reduce cell losses as well as delays for both voice and data. Such a load shedding scheme is expected to improve significantly utilization of B-ISDN.