The relationship between minimum sea level pressure (MSLP) and maximum wind speed, is a commonly employed metric for assessing tropical cyclone (TC) forecast skill. However, accurately reproducing this relationship in TC forecasts is challenging. By introducing a new air-sea momentum flux scheme considering both wave state and saturation (decrease) effect at high winds into a fully coupled atmosphere-ocean-wave model, our numerical results reveal that the maximum wind speed and MSLP respond oppositely to the air-sea momentum flux change. The simulated wind-pressure relationship aligns well with observations when the new flux scheme is used. This study highlights the large sensitivity of wind-pressure relationship to the air-sea momentum flux parameterization at high winds. Furthermore, the air-sea momentum flux has a significant effect on ocean wave characteristics and sea surface temperature (SST) cooling in TC simulations.