This letter studies an energy-efficient unmanned aerial vehicle (UAV)-aided cellular network, where the UAV is dispatched to serve cell edge users in cellular network and helps offload data from the base station by flying with circle path. The goal of this letter is to maximize the energy efficiency of UAV by jointly optimizing resource allocation, user partitioning and UAV trajectory. The formulated problem is shown in a complicated and non-convex form, which is hard to tackle. To this end, the original problem is first decomposed into two sub-problems and then a block coordinate descent method is leveraged, which leads to an efficient iterative algorithm. Simulation results show that the proposed scheme outperforms the benchmarks in terms of the energy efficiency of UAV.