•Spectral fatigue damage prediction of a tripod offshore wind turbine support structure is conducted.•The power spectral density of the hot spot stress is estimated.•The prediction of fatigue damage is evaluated in several spectral fatigue damage models.•The rainflow cycle counting method is assumed to be the “reference” data.•The model that best fits the fatigue damage is identified with the Akaike’s Information Criterion. This work deals with the evaluation of the spectral fatigue damage prediction of a tripod offshore wind turbine support structure subjected to combined stochastic wave and wind – induced loads. The stochastic loadings are defined using the sea states based on a scatter diagram related to the North Atlantic. Further, the power spectral density of the hot spot stress is estimated accordingly. The prediction of fatigue damage is evaluated in several spectral fatigue damage models including the Rayleigh, Wirsching–Light, Tunna, α0.75, Tovo and Benasciutti, Zhao–Baker, Rice and Dirlik models. Critical hot spot locations, which experience the most fatigue damage, are analysed based on the finite element method and the S–N fatigue damage approach. The time-domain solution based on the rainflow cycle counting method is assumed to be the “real” data and the model that best fits the fatigue damage of the wind turbine support structure is identified with the Akaike’s Information Criterion.