The floating offshore wind turbines (FOWTs) have many more advantages than the onshore wind turbines, but they also have more complicated aerodynamic characteristics due to complex platform motions. The research objective of this paper is to investigate unsteady aerodynamic characteristics of a FOWT under the pitch, yaw, and coupled pitch−yaw platform motions using the computational fluid dynamics (CFD) method in the Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. The pitch, yaw, and coupled pitch−yaw motions are studied separately to analyze the platform motions’ effects on the rotor blade. The accuracy of the numerical simulation method is verified, and the overall performances, including power and thrust, are discussed. In addition, the comparison of total aerodynamic performance, force coefficients at different spans and structural dynamic response is provided. The numerical simulation results show that the platform pitching is the main influencing factor of power fluctuation, and the average thrust values of the pitch, yaw, and coupled motions are consistent regardless of the frequency value. The angle of attack (AOA) of airfoils is much more sensitive to the yaw motion, while the blade normal and tangential forces are mainly affected by pitch motion. As for the structural response, the results suggest that the aerodynamic loads of the wind turbine are more sensitive to the pitch motion, which is confirmed by the thrust force and torque of each blade during the platform motions.