This paper presents a pore-scale model proposed for numerical simulation of fines migration in porous media. The model simulates the behavior of spherical particles with different radii in flow by coupling lattice Boltzmann method (LBM) as a computational fluid dynamics (CFD) solver for the simulation of the fluid flow with a rigid body physics engine responsible for the simulation of the particulate transports. To achieve this, the basic LBM algorithm was extended to treat the curved particle boundaries, and a fluid-particle force interaction was implemented in order to account for the exerted force acting on the particles by the fluid and subsequent particulate movements. The accuracy and reliability of the proposed numerical model were successfully validated by simulating Poiseuille flow and Stokes flow and comparing the simulation results with those of the analytical solution. Thereafter, it was employed to simulate the migration of fine particles through synthetic 2D porous media. The simulation results were also presented to investigate the influence of fines migration on the porosity and permeability of the medium, and more interestingly on the hydraulic tortuosity as a criterion for changes in preferential flow path. As will be shown, the developed numerical method is able to successfully capture major retention mechanisms responsible for fines migration associated formation damage including external cake formation by the large particles, internal cake formation by the small particles, pore plugging, and surface deposition. This work provides a framework for further investigations regarding pore-scale phenomena associated with fines migration in the porous media.