A congestion control strategy has been developed in this paper to improve the performance of the network under heavy load It takes two actions; one is a preventive measure and the other is a reactive measure. The preventive measure tracks the link and buffer space utilization. This measure restricts the call's entry into the network beyond the preset level of link utilization. Whenever the buffer gets filled beyond a threshold point, data cells coming in are dropped based on their priority. The reactive measure monitors the buffer space and its utilization Whenever the buffers get filled to a peak value, control cells are generated and are sent to the host computers responsible for buffer overflow. The control cells have a field set to the rate that host computer should use. The new rate set in the control cells is based on the current rate of the call. After reducing the rate, the host will not reduce it further for a period of time called the recovery period that is also based on the current call rate. After the recovery period is over, the host computer will again transmit at the previous call rate.