Atmospheric re-analyses are frequently used to force spectral wave models to develop long-term wave datasets. The accuracy of marine surface winds significantly affects the reliability of the modelled wave fields, especially under wave storm conditions. In this study, we employ the spectral wind-wave model WAVEWATCH III (WW3) forced by ERA5 winds to assess their reliability in modelling extreme ocean waves. A one-year wave hindcast of 2010 is simulated and validated against measurements from both in-situ buoy and altimeter data. The results indicate that ERA5 winds underestimate extreme wave conditions for significant wave heights (Hs) larger than 7.5 m. Accordingly, we present a new wind parameterization, in WW3, that corrects the wind speed bias of ERA5. It has a sigmoid mathematical form showing an exponential growth with a bounded limit of the maximum wind speed to be corrected. The results show that the newly proposed parameterization corrects the negative biases for Hs between 7.5 m and 14 m when compared with the wave measurements. The biases are reduced from - 0.15 m to negligible values in most of the ocean basins. Other hindcast years were also simulated with WW3 using the new parameterization and the outputs were validated against altimeter data, showing reliable results. This confirms the utility of the new parameterization for extreme ocean wave modelling, which is useful for wide offshore and ocean engineering applications.