To improve TCP throughput even if the maximum receiving window size is small, a TCP performance enhancing proxy (PEP) using a UDP-like packet sending policy with error control has been proposed. The PEP operates on a router along a TCP connection. When the PEP receives a data packet from the source host, it transmits the packet to the destination host, copies the packet into the local buffer (PEP buffer) in case the packets need to be transmitted and sends a premature ACK acknowledging receipt of the packet to the source host. In the PEP, the number of prematurely acknowledged packets in the PEP buffer is limited to a fixed threshold (watermark) value to avoid network congestion. Although the watermark value should be adjusted to changes in the network conditions, watermark adjusting algorithms have not been investigated. In this paper, we propose a watermark adjusting algorithm the goal of which is to maximize the throughput of each connection as much as possible without excessively suppressing the throughputs of the other connections. In our proposed algorithm, a newly established connection uses the initial watermark value of zero to avoid drastic network congestion and increases the value as long as its throughput increases. In addition, when a new connection is established, every already-established connection halves its watermark value to allow the newly established connection to use some portion of the bandwidth and increases again as long as its throughput increases. We compare the proposed algorithm (CW method) with other methods: the FW method that uses a fixed large watermark value and the NP method that does not use the PEP. Numerical results with respect to throughput and fairness showed that the CW method is generally superior to the other two methods.