In this paper, we focus on a tandem network, and design an AQMmechanism called FI-RED (Fairness Improvement for RED) for improving the fairness among heterogeneous TCP connections. In FI-RED, ECN (Explicit Congestion Notification) mechanism is used for differentiating the packet marking probability of RED according to the CE (Congestion Experienced) bit of arriving packets. Namely, FI-RED suppresses congestion indication to TCP connections with a large number of hops (i.e., connections with a high probability that the CE bit is marked). With such a simple modification to the original RED, a TCP connection with a large number of hops suffers almost the same packet marking probability as one with a small number of hops. Therefore, it is expected that FI-RED improves fairness among TCP connections with different numbers of hops; i.e., bias against the number of hops. We analyze the steady state behavior of FI-RED and perform simulation experiments in several network configurations. We quantitatively show that the fairness among TCP connections is significantly improved compared with RED.