This paper proposes an explicit rate-based end-to-end congestion control mechanism to alleviate congestion of multimedia traffic in packet switched networks such as the Internet. The congestion is controlled by adjusting the transmission rates of the sources in response to the feedback information from destination such as the buffer occupancy, packet arrival rate and service rate at the outgoing link, so that a desired quality of service (QoS) can be met. The QoS is defined in terms of packet loss ratio, transmission delay, power, and network utilization. Comparison studies demonstrate the effectiveness of the proposed scheme over New-Reno TCP (a variant of AIMD: additive increase multiplicative decrease) technique during simulated congestion. Since it is end-to-end, no router support is necessary, the proposed methodology can be readily applied to today's Internet, as well as for real-time video and voice data transfer in unicast networks.