To understand the flow maldistribution phenomena inside the honeycomb structure of a regenerative burning system, the results from an experimental study of flow distribution in the honeycomb were compared with computation fluid dynamics (CFD) results by means of the Lattice Boltzmann method, which is convenient for simulating fluid flow in complex boundaries. The experimental results of flow distribution agreed well with the CFD results. Although porous plates are often placed in front of the honeycomb structure in order to decrease the maldistribution, our simulation results suggested that porous plates have a limited or opposing effect on flow uniformization. To improve the effect on flow uniformization, it is important to adequately control the pore size distribution on the porous plate while keeping total porosity constant. Calculation of running costs of the regenerative burning system showed that the optimized pore plate can raise the efficiency, while the efficiency of the current honeycomb system was lower than that of the saddle system.