In this paper, we improve the performance of bidirectional TCP connection over end-to-end network that uses transfer rate-based flow and congestion control. The sharing of a common buffer by TCP packets and acknowledgement has been known to result in an effect called ack compression, where acks of a connection arrive at the source bunched together, resulting in unfairness and degraded throughput. The degradation in throughput due to bidirectional traffic can be significant. For example, even in the simple case of symmetrical connections with adequate window size, the connection efficiency is improved about 20% for three levels of background traffic 2.5Mbps, 5.0Mbps and 7.5Mbps. Otherwise, the throughput of jitter is reduced about 50% because round trip delay time is smaller between source node and destination node. Also, we show that throughput curve is improved with connection rate algorithm which is proposed for TCP congestion avoidance as a function of aggressiveness threshold for three levels of background traffic 2.5Mbps, 5Mbps and 7.5Mbps.