In enhanced oil recovery terminology, dispersion refers to the mixing between two stationary or mobile miscible fluids brought together during miscible displacement, which is the result of many different mechanisms, such as molecular diffusion, Taylor effect, viscous fingering effect, and flow behavior around stagnant pockets. Dispersion process in reservoir rocks represents a combination of these mechanisms. In this article, the longitudinal dispersion coefficient is investigated using "Shan-Chen-type multicomponent multiphase lattice Boltzmann," which is a novel and easy way to implement and parallelize a method in computational fluid dynamics. It has shown that the lattice Boltzmann method is a promising approach with a potential capability for simulating fluid flows in different areas. In recent years, it has been used as a very powerful design tool in fluids engineering. The validity of this method is verified with an analytical solution of linear diffusion equation. The flow in fractures and porous medium is then modeled by this approach and the results show that lattice Boltzmann may provide a new route for simulation of miscible displacement.