Recently, the use of Wireless Charging Vehicles (WCVs) to replenish energy for multiple nodes simultaneously has been a research hot spot in Wireless Rechargeable Sensor Network (WRSN). However, existing solutions either ignore the energy demand and its urgency, or only consider them partially in some stages, not during the whole process. There is no an overall solution in which distance and energy information with multiple metrics such as residual energy and demand urgency are jointly considered throughout the whole procedure. To address this problem, an Energy Urgency Priority based Mobile Charging Scheme (EUP-MCS) is proposed. Firstly, the WRSN is clustered by the algorithm of Residual Energy Priority based K-Means (REP-Kmeans++) which brings nodes with less residual energy closer to cluster center. Secondly, the WCV???s optimal docking site at each cluster is selected by the algorithm of Gradient Descent based Anchor Point Selection (GD-APS) according to the nodes??? energy demand weight. Finally, the WCV???s access path is determined by the algorithm of Energy Urgency Priority based Ant Colony System (EUP-ACS) which prioritizes the clusters with high energy demand urgency. Extensive simulation experiments show that REP-Kmeans++ reduces the intra-cluster charging time by 6.4% compared to K-Means, and GD-APS reduces the intra-cluster charging time by 16.5% compared to traditional methods. More comparison experiments reveal that our EUP-MCS scheme outperforms other solutions such as Energy-aware Anchor Point Selection (EAPS), Collaborative Charging Algorithm based on Network Density Clustering (CCA-NDC) and Modified MAX???MIN ant system and Equalization Strategy (MMES) in terms of total traveling distance, death node number, average residual energy and stability.