Abstract: Marine nuclear power platform can provide a stable energy supply for oil and gas exploitation, remote islands and desalination of sea water. It is an important marine equipment with potential. As the core part of the nuclear power platform, the positioning system is mainly composed of a single-point turret, YOKE, mooring legs and mooring bracket, which is a typical multi-rigid body dynamic system. The multi-body dynamic analysis of the positioning system can improve the long-term operation reliability of nuclear power platform. Based on the theory of multi-body dynamics and the topology of multi-hinge connection of positioning system, a multi-body dynamic simulation model of positioning system is established. Then, considering the marine environment of nuclear power platform operation, the 6-DOF motion time history of nuclear power platform under multi-year return periods is obtained through spectral analysis and the theory of linear superposition. Taking the first marine nuclear power platform in China as an example, the mooring restoring force of the positioning system and the mechanical behavior of each hinge joint are calculated under the sea conditions of 1-year return period, 10-year return period and 100-year return period by using multi-body dynamic model. Compared with the quasi-static mechanical model and Kane dynamic model, the mooring restoring stiffness curve of the positioning system is calculated, and the dynamic amplification factor of the mooring restoring force is proposed. The research can provide a reference for the evaluation of the mooring capacity of the positioning system and the mechanical analysis of each hinge structure.