In IEEE 802.11 Distributed Coordination Function (DCF), the multi-rate Basic Service Set (BSS) suffers from the performance anomaly issue, which brings unfairness in terms of channel occupancy time. To solve the issue, this paper presents a rate control scheme for TCP Friendly Rate Control (TFRC) in IEEE 802.11 DCF mode. The proposed scheme controls the sending rate so that each station can use the wireless channel for equal duration. This is based on the channel occupancy period used by each station in BSS, which is monitored at the Media Access Control (MAC) layer. The performance of the proposed scheme over multi-rate IEEE 802.11 DCF is evaluated and compared with that of normal TFRC through several simulations. The simulation results show that the proposed scheme exhibits fairness in terms of channel occupancy time among the competing stations, which accordingly mitigates the performance anomaly. The proposed scheme improves the aggregated throughput in BSS.