In large-scale data centers, two types of network are implemented: local area networks (LANs) and storage area networks (SANs). To achieve simple network management, integration of these two networks by Ethernet technology is of great interest. A SAN requires a significantly low frame loss rate. To integrate LANs and SANs, a multi-hop Ethernet configuration is generally used, and congestion may occur in traffic hot spots. Therefore, layer-2 congestion control that prevents frame loss in multi-hop Ethernet, Quantized Congestion Notification (QCN), is now discussed in IEEE 802.1Qau. In this paper, we evaluate QCN's throughput performance and reveal a technical problem with fairness among active flows. We also propose Adaptive BC_LIMIT for QCN where BC_LIMIT is adaptively decided according to current transmission rate of flows. Simulation results show that our proposed method significantly improves fairness among QCN flows.