The TCP performance can deteriorate substantially in the multipath packet-forwarding networks which induce persistent packet reordering. Focusing on these networks, we propose a simple algorithm to adaptively adjust the value of dupthresh, the threshold of duplicate acknowledgement at which the TCP fast retransmission algorithm is triggered, to improve the TCP performance. It uses an exponentially weighted moving average (EWMA) and the mean deviation of the length of reordering events to adjust the value of dupthresh. Our algorithm also computes an upper bound of dupthresh to avoid retransmission timeout events. In addition, it provides a mechanism to decrease dupthresh at the retransmission timeout (RTO) events. The simulation results show that our algorithm improves the protocol performance significantly with very low overhead. It achieves a greater throughput and fewer false fast retransmissions.