This paper examines the randomness of porous structure composed by cubes or spheres and particle size level in flow and heat transfer characteristics using the 3D lattice Boltzmann method. The simulation results show that randomness has significant effects on permeability and the Nusselt number when the number and size of spheres or cubes are fixed. As the particle size level increases, normalized permeability increases, but the Nusselt number decreases. When the particle size level increases to five, permeability and the Nusselt number cease to change. Furthermore, the effect of porosity for the porous structure with the least number of particle size level on the Nusselt number is the most significant. (C) 2017 Elsevier Ltd. All rights reserved.