In order to improve the data rate of unmanned aerial vehicle base stations (UAV-BS) when serving multiple users on the ground, a deep reinforcement learning (DRL) algorithm was proposed based on dueling deep Q-network (Dueling-DQN). A dueling network (DN) structure was employed to overcome the partially observable problem of the dynamic environment, and the position of the UAV-BS and the power allocation of the downlink were jointly optimized to satisfy the quality of service (QoS) of the ground users. The performance of the algorithm was examined in a more realistic air-ground probabilistic channel model. The results show that compared with the baseline algorithm, the proposed Dueling-DQN algorithm can provide higher data rate and service fairness, and the advantages are more obvious with the increase in the number of ground users. The Dueling-DQN algorithm is effective to solve the complex non-convexity problem, which provides some theoretical reference for the resource allocation problem of UAV-BS.