The unmanned aerial vehicles base stations (UAV-BSs) have great potential in being widely used in many dynamic application scenarios. In those scenarios, the movements of served user equipments (UEs) are inevitable, so the UAV-BSs needs to be re-positioned dynamically for providing seamless services. In this paper, we propose a system framework consisting of UEs clustering, UAV-BS placement, UEs trajectories prediction, and UAV-BS reposition matching scheme, to serve the UEs seamlessly as well as minimize the energy cost of UAV-BSs' reposition trajectories. An Echo State Network (ESN) based algorithm for predicting the future trajectories of UEs and a Kuhn-Munkres-based algorithm for finding the energy-efficient reposition trajectories of UAV-BSs is designed, respectively. We conduct a simulation using a real open dataset for performance validation. The simulation results indicate that the proposed framework achieves high prediction accuracy and provides the energy-efficient matching scheme.