In Molten Salt Reactors (MSRs), the solid fission products are sparingly soluble and in micro-to-nano scale. Their complex behavior are difficult to be accurately modeled by applying traditional Computational Fluid Dynamics (CFD), since CFD is a macro simulation method. Against this background, based on the mesoscopic method of Lattice Boltzmann Method (LBM), we propose a novel approach to analyze the behavior of solid fission products. LBM takes the liquid as discrete microclusters and analyzes their movement by separating it into migration and collision. Statistical tools are used to calculate the microscopic behavior of microclusters with a simple explicit equation, known as the Lattice Boltzmann Equation (LBE). Compared with the CFD, which directly solves the Navier-Stokes equation to simulate fluid behavior, LBE offers several advantages such as easier parallel computing, more straightforward boundary handling and more accurate physical representation. In this paper, LBM is firstly employed to model the classical flow to verify the method via comparing with CFD. The results demonstrate that LBM performs well in computing fluids. Then, we extend LBM to model the migration behavior of solid fission products flowing with the molten salt in the pipes, the obtained results show that the solid fission products tend to be deposited at the inlet and on the lower wall surface. This study would provide a novel, mesoscale-based approach to the study of fission products in MSRs.