The invention relates to a combustion device, in particular to a catalytic flameless combustion device with extremely low pollutant discharge quantity. The flameless combustion device with extremely low pollutant discharge quantity comprises a fuel and combustion-supporting gas inlet, a gas premixer, a combustion plate, an igniter, a gas flow guider, a flameless combustion chamber and a catalyst added therein, a gas collecting chamber and an exhaust opening. The invention provides a method for starting the flameless combustion device with extremely low pollutant discharge quantity. The method comprises the steps of initially utilizing low-power flame combustion to heat the flameless combustion chamber and the catalyst added therein, and increasing the flow velocity to switch into high-power catalytic flameless combustion. The catalytic flameless combustion device can be applied to combustion and heat taking process of various kinds of non-solid fuel, and has the beneficial effects that the fuel is combusted completely, the discharge quantities of a hydrocarbon compound, carbon monoxide and nitrogen oxide in the combustion tail gas are lower than 1 ppm, and the characteristics of high efficiency, energy saving, environmental friendliness, safety, simple structure, high combustion stability and the like are achieved.