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QoS routing in wireless mesh networks (WMNs) is a daunting task. Finding a path for a given flow depends not only on the bandwidth-delay requirements of that flow but also on the available bandwidth of all the nodes in that path and the amount of bandwidth consumption caused by that flow along its path. Contrary to the wired networks, these two parameters are not fixed and depend on the interference pattern of the network that in turn depends on the selected path itself. This converts the QoS routing in wireless mesh networks to a much harder problem. Existing methods use on-demand approach based on flooding of routing packets. This approach does not scale up to large networks. Field-based routing (FBR) is a promising approach to reduce the routing overhead for static route set up. However, it is not previously used for QoS routing. In this paper, we have developed a new FBR based QoS routing protocol for WMNs. Contribution of this paper is two folds. First, a one-pass field-based routing instead of regular two-pass approach is developed that significantly reduces the overhead of distributing routing information and computing the path and increases the QoS delivered to the flows. Secondly, a new routing metric named LU-IR is introduced that is shown to lower intra-flow and inter-flow interferences and results in increased network service capacity. The performance of the proposed algorithm is extensively studied through simulations. The results indicate that average delay of the flows is improved and the network throughput is increased compared to the existing schemes.