Out-of-Plane Bending (OPB) is a special loading condition for mooring chains in offshore engineering, which has led to the fracture of mooring chains in service and caused severe losses. This paper conducts an in-depth analysis of the OPB issue of the mooring chain of the first cylindrical FPSO in Asia, and provides a detailed calculation of the risk of OPB occurrence and the potential fatigue damage it may cause. The analysis results show that the cylindrical FPSO mooring system is affected by OPB, with the first free chain link being the most critical and vulnerable part of the entire mooring system. The calculation results indicate that the fatigue life of the mooring chain is 43.67 years, meeting the reliability requirements of the mooring system. This study is the first in China to carry out the risk analysis of OPB for marine engineering mooring chains, and the proposed assessment method can provide a reference for similar subsequent projects, which has reference significance for improving the reliability and safety of FPSOs.