The aerodynamic performance of floating offshore wind turbines is extremely complex due to the mo-tions of the floating platform. The surge and pitch motions are the most influential motions among the six degrees-of-freedom motions. In view of this, the aim of this study is to investigate the unsteady aerodynamic characteristics of a floating offshore wind turbine under single (surge or pitch) and combined motions using computational fluid dynamics simulations, In addition, the coupling technique of dynamic mesh and sliding mesh is employed, as well as the unsteady Reynolds averaged Navier-Stokes method. The numerical simulation method in this paper is first validated by comparison to the results of the blade element momentum method and the vortex method. Then, the aerodynamic characteristics of the floating offshore wind turbine under harmonic platform motions with different periods and amplitudes are investigated. The results show that the increase of amplitude and frequency aggravate the fluctuation of the overall aerodynamic performance of the wind turbine. In addition, the combined surge-pitch motion reduces the average power generation indicating that complex platform motions adversely affect the power generation of floating offshore wind turbines. (C) 2020 Elsevier Ltd. All rights reserved.