The performance of fibrous air filter media is one of the key factors to influence the indoor air quality. In order to develop low-resistance and high-efficiency media, it is necessary to obtain a realistic media model. Based on the truncated log-normal model, the D2G9 scheme of Lattice Boltzmann (LB) method was applied to predict both the resistance and the filtration efficiency of the flow through microscale porous media. The influences of the boundary conditions were investigated. The slip and no-slip boundary conditions on fiber surfaces, as well as the non-equilibrium extrapolation scheme and the periodic scheme, were included in this study. By validating the simulated results with both the experimental and empirical values, it was found that the simulated resistance with the slip boundary on fiber surface and the periodic scheme on upper/lower walls was closer to the real value. The model established in this paper and the LB method presented here provide support for further research on optimization of the fibrous air filter media.