Liquefied nature gas (LNG) is a green energy. LNG-fueled vessels are extremely complex engineering systems. In view of the inherent hazardous properties of LNG fuel, LNG fueling is not only an important part, but it is also full of high risks in the operation of LNG-fueled vessels (LNGFVs). Therefore, it is necessary to study the risk factors, and the intrinsic relationship among them between the LNG and the vessel, and to simulate the system dynamics in the process of LNGFV operation. During the process of fueling of LNGFV, at every moment the vessel interacts with the energy and information of the surrounding environment. First, the impact of the three interactions of the fueling operation process, ship factors, and environmental factors were analyzed on the risk of fueling operation, and a complete node system was proposed as to the complex system dynamics mode. Second, by analyzing the boundary conditions of the system, the relationship of factors was established via the tools of system dynamics (SD). Based on the catastrophe theory (CA), the dynamics model for the fueling of LNG is set up to study the system’s risk mutation phenomenon. Third, combined with the simulation results of the case analysis, the risk evolution mode of the LNGFV during the fueling process was obtained, and constructive opinions were put forward for improving the safe fueling of the LNGFV. Application examples show that formal description of risk emergence and transition is a prerequisite for the quantitative analysis of the risk evolution mode. In order to prevent accidents, the coupling synchronization of risk emergence should be weakened, and meanwhile risk control should be implemented.