A hybrid system consisting of a spar-type wind turbine and an annular wave energy converter (WEC) is prospective in joint offshore wind-wave energy exploitation. Its coupled dynamic and power features in vast operating sea states are a valuable reference for design but are poorly understood. This study aims to fill the gap. By combining the wind module of OpenFAST and an in-house code, a numerical tool that can tackle the full aero-servo-hydro-mooring couplings in the hybrid system is developed. Dynamic features, mooring tensions, and energy conversion performance of a Hywind-annular WEC hybrid system are analyzed in a wide range of operating conditions with varying speeds of steady winds and periods of regular waves, emphasizing the effect of the annular WEC on the dynamic and power performance of the Hywind. Results show that the annular WEC improves the wind power generation below the rated wind speed and the stability of the Hywind by reducing its pitch displacement. But it also increases the motion amplitude in the heave direction. The annular WEC has a neglectable influence on the maximum mooring tensions. An evaluation of the annual wind-wave power based on hindcast sea states shows that wave power can effectively supplement wind power.