The invention relates to a low-nitrogen combustion garbage incinerator and a combustion method. The garbage incinerator comprises a garbage incinerator grate and a flue, wherein the garbage incinerator grate is positioned in a hearth; and the flue is positioned above the front end of the garbage incinerator grate. The garbage incinerator is characterized by further comprising a first extraction opening and a main air duct pipe; the first extraction opening is formed above the hearth at the tail end of the garbage incinerator; the two ends of the main air duct pipe are respectively communicated with the first extraction opening and the flue; and a cyclone separator is also arranged at one end, close to the first extraction opening, of the main air duct pipe, and is used for purifying flue gas extracted from the first extraction opening and spraying the purified flue gas in the flue. The low-nitrogen combustion garbage incinerator and the combustion method have the advantages that (1) the discharges of NOX and flying ash generated by the incinerator are reduced synchronously; and (2) the dust content in the flue of a low-nitrogen combustion system and a draught fan is reduced greatly, so that the possibilities of dust collection and wear are low, and the service life of the low-nitrogen combustion system is prolonged.