Catenary mooring lines used in floating offshore platforms are a representative structural part that undergoes a wide-banded tension process due to low frequency drift forces and high frequency wave forces. Time domain analyses are the best way to determine a representative fatigue damage under a wide-banded process, but the time domain analysis can be computationally expensive. This paper reports a functional relationship between the environmental conditions and probability density function (PDF) of tension distribution using an Artificial Neural Network (ANN), which can be used to reduce computational cost with reasonable accuracy when compared to the time domain approach. The predictive accuracy of the fatigue damage under wide-banded process is dependent on how well the PDF of the process is defined. This study addresses three approaches in expressing the distributions: superposition of multiple Gaussian distribution functions (Superposition approach), direct prediction of the distributions (Piecewise approach), and nth-order moments of the distributions (Moment approach). A full-scale floating offshore wind turbine (FOWT) platform was used for the target structure with three catenary mooring lines. The sea state data collected from the Jeju offshore area in Korea were used as the input data for the time-domain mooring dynamics analyses of the FOWT as well as input neurons of the three multi-layered ANN models. The tension distributions in each mooring line were used for the three types of output neurons in terms of the PDF parameters for the Superposition approach, a certain number of distribution points for the Piecewise approach, and moment values for the Moment approach. The accuracy of each trained ANN was verified by comparing the predictions by the trained ANN with the hydrodynamic simulation results for the newly defined load cases. It was proven that the Moment approach-based ANN model predicts the wide-banded fatigue damages most consistently.