Multimedia communications over Internet should achieve adequate quality of service while maintaining 'fairness' in network resources allocation with respect to competing connections. To achieve these conflicting requirements the adopted transport protocol should provide an adequate average throughput and implement congestion control and flow control mechanisms designed to minimize packet loss, delay and throughput variations. The transport protocol proposed here is a modified version of the window-based datagram congestion control protocol, that implements a TCP-like congestion control mechanism wherein the multiplicative decrease of the congestion window is controlled by a non-linear function. Experimental results show that this modified congestion control algorithm, which is adjusted at run-time based on the estimated mean round-trip time, is good candidate toward the aforementioned requirements.