In order to research macroscopic mass transport characteristics of porous media, a lattice Boltzmann method (LBM) approach was utilized to calculate asymptotic longitudinal mass dispersion. In this study, a D2Q9 model with multi-relaxation-time (MRT) collision operator, which is appropriate for incompressible flow with a high Péclet number without refining the lattice, was chosen. With respect to the microstructure of porous media, random placement (RP) method was applied to obtain randomly positioned particles. Based on the exhausted numerical results presented in the study, a new correlation of longitudinal mass dispersion was established. By comparing with available experimental data in the literature, reasonable agreements are observed in a wide porosity range from 0.3 to 0.7, indicating the validity of the proposed correlation.