Abstract: Due to the sway motion of the floating platform,the aerodynamics of floating wind turbines is highly complex compared to the fixed based wind turbines. In the present paper,a lifting surface method with free wake model was developed to study the unsteady aerodynamic performance of the NREL 5 MW floating wind turbine under prescribed sway motions. The results showed that under platform sway motion,the induced velocity from the free wake decreased and both the power output and the rotor thrust level increased compared to the fixed based wind turbine. The variation of the root load on the blade showed a two times frequency on the sway motions.The increased load on the blade may increase the possibility of the collision between the blade tip and the tower.