Recently, the implementation of federated learning (FL) in wireless networks becomes a hotspot due to its flexible collaborative learning methods and privacy-preserving benefits. However, most of the existing works overlook the impact of user mobility on the learning performance, which is critical. Specifically, the mobile users may roam among multiple edge access points (APs) during the local training procedures, leading to incompletion of inconsistent FL training. In this paper, we theoretically study the impact of user mobility on the FL in hierarchical wireless networks. In our system model, the network consists of one cloud server, several edge APs, and multiple mobile users that have their positions vary over time. During the local training process, users may stay in or move out of the coverage area of the originally attached edge AP. In such a practical context, we analyze the convergence rate of the FL algorithm and provide experiments to evaluate the learning performance under different network parameters. Our results provide insights in further improvements of FL in hierarchical wireless networks.