In this study, effects of damage levels of fiber ropes on the performance of a hybrid taut-wire mooring system are investigated. The analysis is performed using a numerical floating production storage and offloading (FPSO) model with a hybrid mooring system installed in 3000 m of water depth. An in-depth study was conducted using the numerical model, the dynamic stiffness equation of damaged fiber ropes, the time-domain dynamic theory, the rainflow cycle counting method, and the linear damage accumulation rule of Palmgren-Miner. Results indicate that, in a mooring line with an increasing damage level, the maximum tension decreases, while the offset of the FPSO increases. Particularly, when a windward mooring line failure occurs, in addition to the significant increase in the offset of the FPSO, the maximum tension, tension range, and annual fatigue damage levels of the remaining lines adjacent to the failed also increase significantly. The present work can be of great benefit to the evaluation of the offset of the floating platform, the tension response, and the service life of the hybrid mooring systems.