Fatigue damage assessment for marine structures subjected to various random environmental loadings is an important issue at the design stage. In many situations, the responses of marine structures present wide-band and non-Gaussian properties. In this paper, a neural network model was developed to predict the fatigue damage caused by wide-band non-Gaussian random processes. Many power spectra with different values of bandwidth parameters, inverse slope of the S-N curve, and skewness and kurtosis of non-Gaussian processes were used to train and validate the developed neural network model. In order to determine the optimal neural network structure, the effects of input neurons, the numbers of hidden layer neutrons and hidden layers on the prediction accuracy were investigated. Through case studies with realistic bimodal spectra, by taking the fatigue damage estimated by time-domain rain-flow counting method as reference, it is demonstrated that the developed neural network model is more accurate and robust than the existing frequency-domain methods for fatigue damage assessment of wide-band non-Gaussian random processes.