A highly efficient nonlinear frequency-domain solution method is proposed and employed to investigate the aerodynamic and aeromechanical performances of an oscillating wind turbine blade aerofoil in this study. Extensive validations of a frequency-domain method against an experiment as well as a typical time-domain solution method are provided in this paper. An experiment is also designed and conducted to measure pressure distributions over an aerofoil as well as to validate the numerical model. Unsteady pressure distributions and aeroelasticity parameters of the oscillating NACA0012 aerofoil are computed at various angles of attack and Reynolds numbers. Results indicate that the difference of unsteady pressure distributions between the two surfaces of the aerofoil becomes larger as the angle of attack is increased, whereas the flow separation on the suction surface is reduced by raising the Reynolds number. The turbulent flow develops in the downstream region due to the laminar vortex shedding at lower Reynolds numbers. It is also revealed that the Reynolds number has an impact on the aeroelasticity, and the aerodynamic damping value is larger at higher Reynolds numbers. The comparison between the frequency-domain method and the time-domain method shows that the frequency-domain method is not only accurate but also computationally very efficient as the computation time is reduced by 90%.