Different from previous works, this paper considers the router node placement of wireless mesh networks (WMNs) in a dynamic network scenario in which both mesh clients and mesh routers have mobility, and mesh clients can switch on or off their network access at different times. We investigate how to determine the dynamic placement of mesh routers in a geographical area to adapt to the network topology changes at different times while maximizing two main network performance measures: network connectivity and client coverage, i.e., the size of the greatest component of the WMN topology and the number of the clients within radio coverage of mesh routers, respectively. In general, it is computationally intractable to solve the optimization problem for the above two performance measures. As a result, this paper first models a mathematical form for our concerned problem, then proposes a particle swarm optimization (PSO) approach, and, from a theoretical aspect, provides the convergence and stability analysis of the PSO with constriction coefficient, which is much simpler than the previous analysis. Experimental results show the quality of the proposed approach through sensitivity analysis, as well as the adaptability to the topology changes at different times.