Unstable flow within a reactor coolant pump (RCP)’s mechanical seal may cause the change of its sealing parameters, possibly threatening RCP’s safe operations. In this study, based on the moving grid technology, a 3D fluid–structure interaction analysis model is established, where the influence of parameters such as the inlet pressure fluctuation, closing force fluctuation, and speed fluctuation on mechanical seal performance characteristics within an RCP is numerically studied. Study results have shown that when pressure and closing force fluctuations are applied, the static ring displacement, the inlet-to-outlet temperature difference, and the leakage difference show similar variational rules. In addition, it is found that the sealing parameters are more sensitive to the step form of fluctuation. When the step change of 4% closing force was applied, the static ring displacement was more than 36.7%, the change of the temperature difference between inlet and outlet zones exceeded 53.5%, and the leakage difference was more than 127.2%. The change of speed has also been found to significantly affect the temperature difference between the RCP mechanical seal’s inlet and outlet, but the effect on the leakage and opening force was negligible.