This paper investigates the problem of unmanned aerial vehicle (UAV) aerial refueling docking control subject to system model uncertainties and multiple disturbances. The control of aerial refueling docking can be regarded as the problem of precise trajectory tracking of probe-drogue refueling (PDR) under various disturbances. Different from the traditional backstepping control, adaptive dynamic surface control (ADSC) avoids the “differential expansion” in the derivation process of virtual control, which greatly simplifies the difficulty of controller design. Then, a novel ADSC strategy based on radial basis function neural network (RBFNN) is proposed to improve the anti-disturbance performance and docking control accuracy of PDR system. Finally, the effectiveness of the proposed control method is verified by digital simulation.