We preformed 2D pore-scale numerical simulation of a two-layer porous burner with staggered arrangements of connected particles. Solid-to-solid radiant heat exchange is taken into account by discrete ordinates (DO) model and solid conduction between the adjacent particles is considered using bridge approach. The predictions show that the distributions of temperatures, species and velocities within pores in the burner are highly two-dimensional. The root mean squares of solid temperature is used to quantitative study thermal nonequilibrium inside solid particles. Results show that thermal nonequilibrium exists over the entire burner and varies along the flow direction. The root mean squares of solid temperature is wave-like shape for different inlet velocities and equivalence ratios. From the burner inlet, the root mean squares of solid temperature increases slightly in the preheating zone and rapidly increases to its maximum in the reaction zone, then decreases sharply to a small value. This value is almost a constant from the thermal relaxation zone to the burner outlet. The extent of thermal nonequilibrium in the reaction zone increases as inlet velocity is increased or the equivalence ratio is decreased. For reaction flow, the pressure loss in the structured burner is smaller than that of random packing bed for the whole investigated range of inlet velocity. Numerical results are validated against experiment data.