In order to guarantee the bandwidth of a flow (flow QoS) in Wireless LANs (WLANs), a flow QoS guarantee method using both TCP Congestion Control for QoS (QoS-TCP) and MAC Frame Priority Control (QoS-MAC), which we refer to as a cross layer control method, has been proposed. This method tries to guarantee the bandwidth of a flow mainly by using QoS-TCP. And MAC Frame Priority Control assists with QoS-TCP to guarantee the bandwidth. This paper uses TCP-AV and Receive Opportunity Control in MAC Frame (ROC) as QoS-TCP and QoS-MAC, respectively. The previous study evaluates the cross layer control method in a single rate environment. In this environment, each terminal uses only one transmission rate in the physical layer. However, current wireless devices usually use multiple transmission rates. This study calls this environment as a multi-rate environment. Thus, the performance evaluation of the cross layer control method over the multi-rate environment is insufficient. This paper evaluates the throughput performance of the cross layer control method in the multi-rate environments. Moreover, this paper shows that the method can assure the target bandwidth in the multi-rate environment. From simulation results, we found that the method can guarantee the target bandwidth for a priority flow and improve the total throughput in the multi-rate environment.