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In this paper we present a new cross-layer method for the routing problem in Wireless Mesh Networks taking into account the Quality of Service (QoS) with rate adaptation. Since different routing metrics play certain importance in the multihop routing, multiple objectives such as transmission delay, traffic load and bandwidth are incorporated to the routing metric. Meanwhile a new link-layer sensing technique enables the transmitter to acquire the current contention status with low overhead, and rate adaptation is considered in the routing discovery. Theoretical analysis and simulation results show that the proposed QoS-Aware HWMP has a better average end-to-end delay guarantees and bandwidth guarantees.