This paper presents a fair and efficient rate control mechanism, referred to as congestion-aware fair rate control (CFRC), for IEEE 802.11s-based wireless mesh networks. Existing mechanisms usually concentrate on achieving fairness and achieve a poor throughput. This mainly happens due to the synchronous rate reduction of neighboring links or nodes of a congested node without considering whether they actually share the same bottleneck or not. Furthermore, the achievable throughput depends on the network load, and an efficient fair rate is achievable when the network load is balanced. Therefore, existing mechanisms usually achieve a fair rate determined by the mostly loaded network region. CFRC uses an AIMD-based rate control mechanism which enforces a rate-bound to the links that use the same bottleneck. To achieve the maximum achievable rate, it balances the network load in conjunction with the routing mechanism. Furthermore, it allows the intra-mesh flows to utilize the network capacity, and the intra-mesh flows achieve a high throughput. Finally, we investigate the performance of CFRC using simulation in ns-2, and the results demonstrate that CFRC increases the throughput with the desired fairness.