The QoS performance of wireless mesh networks (WMNs) is measured by the topology connectivity as well as the client coverage, both of which are related to the problem of router nodes placement, in which each mesh client is served as equal. In practice, however, mesh clients with different payments for the network services should be provided by different qualities of network connectivity and QoS. As a result, to respond to the practical requirement, this paper considers the router nodes placement problem in WMNs with service priority constraint in which each mesh client is additionally associated with a service priority value, and we constrain that the mesh clients with the top one-third priority values must be served. Our concerned problem inherited from the original problem is computationally intractable in general, and hence this paper further proposes a novel simulated annealing (SA) approach that adds momentum terms to search resolutions more effectively. Momentum terms can be used to improve speed and accuracy of the original annealing schedulers, and to prevent extreme changes in values of acceptance probability function. Finally, this paper simulates the proposed novel SA approach for different-size instances, and discusses the effect of different parameters and annealing schedulers.