In order to study the dynamic response characteristics of the cylindrical FPSO mooring system, the basic parameters of the cylindrical FPSO "HYSY 122" and its mooring system are used. A full-coupling analysis model of the FPSO and its mooring system are established by using the offshore finite element analysis software OrcaFlex, and the maximum tension of each mooring line of the mooring system is calculated by the concentrated mass method. The mooring system of the ballast and fully loaded FPSO is safely checked under once-in-a-century environmental conditions. The results show that all the structures of mooring line meet API strength standards. All the mooring lines that bear the maximum tension in the approach direction. The tension of each structure of the anchor chain 4 under the ballast condition is the largest, and the tension of each structure of the anchor chain 5 under the full load condition is the largest. The maximum lateral displacement of the FPSO under the full load condition and the ballast condition is greatly different between the wind and wave azimuth angles of 115°~135°, and the remaining azimuth angles are basically consistent. The research can provide some reference for the engineering practice of cylindrical FPSO mooring system.