The present invention relates to a combustion apparatus, and in particular to a catalytic flameless combustion apparatus with extremely low pollutant emission. The apparatus comprises a fuel inlet, a combustion-supporting gas inlet, a gas premixer, a combustion plate, an igniter, a gas deflector, a flameless combustion cavity, a catalyst filled in the flameless combustion cavity, a gas collection chamber and an exhaust port. The present invention describes a method for starting the catalytic flameless combustion apparatus with extremely low pollutant emission, comprising initially combusting and heating the flameless combustion cavity and the catalyst filled therein with low power flame; and then increasing flow velocity and switching to high power flame for conducting catalytic flameless combustion. The catalytic flameless combustion apparatus of the present invention can be used for various non-solid fuel combustion and heat extraction processes. The beneficial effects are: the fuel is completely combusted; and the emissions of hydrocarbon compound, carbon monoxide and nitrogen oxide in combusted tail gas are lower than 1 ppm. The catalytic flameless combustion apparatus has the characteristics of high efficiency, energy saving, environmental protection, safety, simple structure, good combustion stability, etc.