Molten Salt Fast Reactors (MSFR) exhibit excellent performance in nuclear proliferation resistance and nuclear waste transmutation. Source term calculation is a critical factor in reactor operation, especially in Liquid-Fueled Molten Salt Reactors (LF-MSRs). In view of the complex dynamic behavior of source terms in LF-MSRs, it is essential to account for interdependent physical phenomena in the analysis, thereby improving radiation shielding design and safety assessments for LF-MSRs. A multi-physics coupled source term calculation model is proposed in this study, integrating nuclide transport, thermal hydraulics, burn-up, and neutron transport, with the aim of capturing the evolution and distribution of source terms in LF-MSRs, while addressing key physical phenomena in MSFRs. Subsequently, numerical simulations were performed based on a simplified MSFR model at different burn-up stages to calculate the source terms, and to analyze the yield and distribution of fission products. The results demonstrate that the proposed source term model accurately simulates the behavior of source terms at various burn-up depths, effectively capturing the complex physical processes under actual reactor operating conditions. This research provides a solid foundation for the precise assessment and control of radioactive materials, contributing to more effective radiation shielding design and enhancing the safety and controllability of LF-MSRs.