A catalytic combustor burns a fuel-air mixture which is not preheated. The combustor includes a strip or strips of metal which define a plurality of alternating wide and narrow channels. The channels contain corrugated strips which maintain the spacing of the channels. A catalyst coating is deposited only in the wider channels, the narrower channels remaining un-catalyzed. The strip or strips can be heated resistively to start the combustion. Once the combustion is started, the electric current is stopped, and the combustion continues. The combustor is useful in a home heating appliance such as a gas furnace. In another embodiment, in which the combustor is used in a high-temperature environment such as in a gas turbine, the catalyst can be deposited in the small channels only, so as to limit the amount of catalytic combustion.