In modern aircraft design, numerical simulation becomes an important way to study the aerodynamics of aircraft because of its low cost, high efficiency and high flexibility. In the aerodynamic analysis of rotor unmanned aerial vehicles (UAVs), due to the interaction between rotor and fuselage, we have to model the full rotor UAVs, including the rotor and fuselage, to obtain accurate simulation results. In this kind of simulation, a key step is to effectively model the relative motion between the rotor and fuselage, which is a great challenge. In this paper, a highly scalable parallel computing method based on unstructured sliding meshes for the aerodynamic simulation of rotor UAVs was designed. In the proposed method, an unstructured moving mesh finite element method was used to discretize the governing equations in space, a fully implicit second-order backward differentiation formula was adopted for the temporal discretization, and finaly a parallel Newton-Krylov-Schwarz method was introduced to solve the discritized nonlinear equations. As a case study, we have tested the algorithm on the Tianhe II supercomputer for a rotor UAV in the hover state, and obtained some detailed flow information. Performance results show a nearly linear speedup for up to 4 096 processor cores, suggesting that our solution lays a good foundation for fast and high-fidelity aerodynamic simulation of rotor UAVs.