The damage detection of mooring lines is critical to safe operations because the stability of offshore floating platforms depends on the integrity of such lines. However, existing mooring line damage detection techniques are considerably limited because they cannot be implemented constantly. To resolve this inadequacy, this paper proposes a deep-learning-based approach that can detect underwater mooring line damage based on the real-time monitored response data of floating structures. Catenary mooring lines, one of the most widely applied types for floating offshore structures, are selected for the study. In the proposed approach, the detection model of catenary mooring line damage uses both the response data generated through the simulation of the floating structure and the corresponding environmental condition data. In particular, a recurrent neural network (RNN) that can effectively analyze the time-series continuity of the response data is employed for damage detection. The results of the RNN-based catenary mooring line damage detection approach proposed in this study confirm that the RNN model exhibits minimum and maximum detection accuracies of 99.59% and 99.99%, respectively, regardless of whether the measurement data include errors. These detection accuracies indicate that the proposed approach can be used to determine mooring line damage under actual field conditions.