The invention discloses a spraying-absorbing-type method and a spraying-absorbing-type device for waste heat recovery, desulfurization and denitration of fuel-gas flue gas. The fuel-gas flue gas firstly enters a desulfurization and denitration module, and then enters a latent-heat recovery spraying module in n-level series connection after being cooled, desulfurized and denitrated, and outlet air is exhausted to a chimney after the flue gas directly contacts with spray water and is cooled and condensed for n times; an independent cold water circulation is formed in the latent-heat recovery spraying module in n-level series connection, circular-flow direction of the cold water is opposite to the flow direction of the flue gas, and the temperature of the spray water in the latent-heat recovery spraying module serially connected along the flow direction of the flue gas decreases level by level; independently circular cold water is produced by a fuel-gas-driven absorption refrigerating machine; complete sensible heat and most of latent heat of the flue gas are used for heating primary return water, and SO2 (sulfur dioxide) and NOx (nitrogen oxides) in the flue gas are effectively absorbed by the spray water, so that pollution of the flue gas to environment is reduced. The occupied space of the device is effectively saved, the device is compact in structure, pipeline production cost and delivery energy consumption are saved, and construction technique is simplified.