The mooring lines of a floating type offshore plant are known to show wide banded and bimodal responses. These phenomena come from a combination of low and high frequency random load components, which are derived from the drift-restoring motion characteristic and wind- sea, respectively. In this study, fatigue models were applied to predict the fatigue damage of mooring lines under those loads, and the result were compared. For this purpose, seven different fatigue damage prediction models were reviewed, including mathematical formula. A FPSO (floating, production, storage, and offloading) with a $4{ imes}4$ spread catenary mooring system was selected as a numerical model, which was already installed at an offshore area of West Africa. Four load cases with different combinations of wave and wind spectra were considered, and the fatigue damage to each mooring line was estimated. The rain flow fatigue damage for the time process of the mooring tension response was compared with the results estimated by all the fatigue damage prediction models. The results showed that both Benasciutti-Tovo and JB models could most accurately predict wide banded bimodal fatigue damage to a mooring system.