Abstract: We propose in this paper a new policy for TCP congestion avoidance and we compare, by a queueing-simulation study, its performances to those of standard policy. This last leads to unfair sharing of bandwidth when multiple connections, with different round trip times (RTTs), traverse the same bottleneck link with the long RTT connections obtaining only a small fraction of their fair share of the bandwidth. The new policy, which we refer to "CANIT" (Congestion Avoidance with Normalized Interval of Time), allows TCP senders of all connections sharing the same network resource to accelerate their rates similarly during congestion avoidance phase. Our first main result is that, using "CANIT" algorithm, instead of the standard congestion avoidance one, improves the TCP fairness as well as the utilization of network resources. And our second main result is that, using the small values of the parameter "NIT" (Normalized Interval of Time) in our algorithm leads to more efficient use of bandwidth and the fairness is more improved.