To develop renewable energy, the offshore wind energy technology has become an attractive research field. Considering the coupling effect of the platform motions and aerodynamic loads, how to accurately simulate the aero-hydrodynamics of floating offshore wind turbine is important. In this paper, an unsteady actuator line model (UALM) coupled with a two-phase CFD solver called naoe-FOAM-SJTU is applied to solve the three-dimensional Navier-Stokes equations to focus on the coupled dynamic responses of an aerodynamics-hydrodynamics-mooring system for a floating offshore wind turbine named OC3-HywindSpar under extreme sea conditions. Response characteristics including the thrust and the rotor power of the wind turbine, the motions of the platform and the mooring loads under different extreme sea states are carefully compared to study the influence of the wind speed and the wave height on the floating offshore wind turbine. Furthermore, several conclusions are drawn based on the comparison results.