The present invention provides a burner combustion method for supplying and combusting an oxidant stream and a fuel stream, wherein the oxidant stream is composed of a primary oxidant stream jetted from around the periphery of the fuel stream or from a position near the fuel stream, and a plurality of secondary oxidant streams, and by periodically changing the flow rate of at least one of the primary oxidant stream and the plurality of secondary oxidant streams, and also causing a periodic change in the oxygen concentration within the oxidant stream, causing a periodic change in the oxygen ratio which is calculated by dividing the supplied amount of oxygen, supplied by the oxidant stream, by the theoretically required amount of oxygen, and providing a difference between the periodic changes in the oxygen concentration and the oxygen ratio, the combustion state adopts a periodic oscillating state.