Laminar premixed flame inside a honeycomb ceramic is investigated experimentally and theoretically to provide the detailed data for computational approaches and to further the physical understanding of the involved mechanisms of heat transfer, particularly such as the internal heat-recirculation. The ranges of flammability and flame stability are substantially extended without any external heating. Two types of stable flame are observed; one is nearly one-dimensional in the combustor, and the other highly two-dimensional. These are also clearly distinguished by the soot lines observed in the cross-section of the combustor, and correspond to the upper and lower solutions of the theoretical analysis. Temperature measurements show the higher gas temperature than the adiabatic flame temperature, which is attributed to the internal heat-recirculation. The analysis based on the one-dimensional flame theory reproduces reasonably the experimental temperature profiles and flame behaviors, and reveals that heat is recirculated to the unburned mixture both by the conduction and the radiation of solid phase. The stable flame is also predicted in the downstream region of the combustor but not observed in the experiment presumably due to the two-dimensional effects of heat loss. A noticeable result of this work is the existence of the flame of low burning velocity and low temperature, which is different from the excess enthalpy flame.