NOVELTY - A landfill gas is subjected to temperature swing adsorption by removing impurities in cyanide adsorbent tower. The gas is heated and deoxygenation reaction is carried out in sulfur-resistant catalyst bed. The deoxygenated gas is cooled to room temperature, to obtain sulfur compound-containing gas. The gas is cooled to room temperature, and supplied to deacidification adsorption column and subjected to deacidification selection pressure swing adsorption and cryogenic separation method. Thus, the purification and extraction of methane in waste landfill gas are carried out.    USE - Method of purifying and extracting methane in waste landfill gas (claimed).    ADVANTAGE - The method enables purification and extraction of methane in waste landfill gas, with high methane recovery rate, stable device operation, high reliability and heat utilization rate, low energy consumption and reduced emissions. The industrial effluent gas is efficiently recycled.    DETAILED DESCRIPTION - A landfill gas is pressurized at atmospheric pressure of 0.1 MPa by fans, and pressurized to 0.2-2.5 MPa using compressor. The landfill gas is subjected to temperature swing adsorption by selecting alumina and silica or alumina and activated carbon as adsorbent, passing gas from two parallel positions through absorber, switching different periods of tower through a valve, passing raw material gas through tower, feeding sulfur as feed gas, removing impurities chosen from phosphorus and arsenic in cyanide adsorbent tower, regenerating adsorbent tower, and desorbing adsorbed impurities. The gas is heated at 200-400 degrees C and supplied to deoxygenation reactor and deoxygenation reaction is carried out in sulfur-resistant catalyst bed. Oxygen gas is removed to 0.2 vol.% or less. The conversion rate of impurities e.g. sulfur, phosphorus, arsenic and cyanide in gas is 2000-15000 hour-1. The deoxygenated gas is cooled to room temperature, to obtain sulfur compound-containing gas having total sulfur content of 1000 mg/m3. The catalyst is recycled, and oxygen in the feed gas is removed. The gas is cooled to room temperature, and supplied to deacidification adsorption column and subjected to deacidification selection pressure swing adsorption, caustic method, methyldiethanolamine method or low-temperature methanol wash method, and concentrate pressure swing adsorption process or cryogenic separation method. Thus, the purification and extraction of methane in waste landfill gas are carried out.