The permeability coefficient of seepage is an important factor that is widely used in various engineering fields. There are numerous issues that influence the permeability coefficient, among which the porosity, particle size, particle size distribution and Reynolds number are of great importance. In this paper, a C++ code based on the three-dimensional lattice Boltzmann method (LBM) was developed and used to investigate the effects of the abovementioned factors on the permeability coefficient. A multiple relaxation time (MRT) collision scheme of the LB equations was used in the simulation. Porous media were prepared using the random packing method. Laminar flow and turbulent flow were simulated separately for particle Reynolds numbers in a range from 0.001 to 3,000. It was proven that in addition to the influence of porosity and particle size distribution on the permeability, the influence of the Reynolds number was obvious and could not be ignored. As the Reynolds number increased, the permeability of porous media decreased gradually. Based on the numerical simulation results, a modified formula for the permeability coefficient is proposed.