The permeability of random porous media composed of multi-sized particles is calculated by using the lattice Boltzmann method. This paper studies the randomness of porous structure, particle size level and particle shape on flow characteristics. Results show that randomness has significant effects on permeability when the number and size of spheres or cubes are fixed, especially for the cubes. As the particle size level increases, the normalized permeability increases. When the size level increases to five, the permeability does not continue to increase. Furthermore, this paper studies the effect of particle shape on flow characteristics. The results show that the normalized permeability of sphere particle is larger than cube particle. In addition, our research results extend studies to a case where the cube length is smaller than the cube height. (C) 2016 Elsevier Ltd. All rights reserved.