Wireless rechargeable sensor networks (WRSNs) have become a hot research issue owing to the breakthrough of wireless power transfer (WPT) technology. Previous theoretical schemes are mostly designed for 2-D networks, and few of them are tailored for 3-D scenarios, making them not suitable for wide adoptions in practical applications. In this paper, we address the issue of how to serve a 3-D WRSN with an unmanned aerial vehicle (UAV). Our main concern is to maximize the charged energy for sensors supplied by the UAV, which has energy constraints. We respectively develop a spatial discretization scheme to construct a finite feasible set of charging spots for the UAV in a 3-D environment and a temporal discretization scheme to determine the appropriate charging duration for each charging spot. Then, we reduce the problem into a submodular maximization problem with routing constraints and present a cost-efficient algorithm (CEA) with a provable approximation ratio to solve it. Finally, test-bed experiments are conducted to show the feasibility of our schemes in practical scenarios. Extensive simulations are taken to verify the superior performance of our algorithm in charged energy and robustness. The charged energy of our scheme outperforms other competing methods by at least $18.2\%$.