To resolve the flow maldistribution phenomena inside the honeycomb structure of a regenerative burning system, turbulent flow in the honeycomb structure was numerically simulated by the Lattice Boltzmann method. A new technique was proposed to automatically design the pore size distributions of the pore plate in front of the honeycomb while keeping the total porosity of the plate constant. In consequence, the technique had an effect on flow uniformization, especially in the case of horizontal inlet of flow with an adequate entrance region. The proposed technique also showed that the coefficient of variation, which represents the uniformity of the flow velocity, could be reduced to 0.3-0.4, while our target value for the coefficient of variation for 3/4 saddle was 0.5.