This paper proposes a congestion avoidance algorithm which provides stable throughput and transmission rate regardless of buffer size by limiting the TCP congestion window in fixed bandwidth networks. Additive Increase, Multiplicative Decrease (AIMD) is the most commonly used congestion control algorithm. But, the AIMD-based TCP congestion control method causes unnecessary packet losses and retransmissions from the congestion window increment for available bandwidth verification when used in fixed bandwidth networks. In addition, the saw tooth variation of TCP throughput is inappropriate to be adopted for the applications that require low bandwidth variation. We present an algorithm in which congestion window can be limited under appropriate circumstances to avoid congestion losses while still addressing fairness issues. The maximum congestion window is determined from delay information to avoid queueing at the bottleneck node, hence stabilizes the throughput and the transmission rate of the connection without buffer and window control process. Simulations have performed to verify compatibility, steady state throughput, steady state packet loss count, and the variance of congestion window. The proposed algorithm can be easily adopted to the sender and is easy to deploy avoiding changes in network routers and user programs. The proposed algorithm can be applied to enhance the performance of the high-speed access network which is one of the fixed bandwidth networks.