The invention discloses an absorber catalyst containing vanadium pentoxide, Ti02 and activated charcoal and a method of purifying smoke and gas under microwave radiation with the catalyst. The catalyst mainly composed of an activated charcoal base with absorption function, a Ti02 carrier with a high specific surface area and a vanadium pentoxide active component with strong oxidizing performance. As the microwave can take strong assisting and catalysis effect to chemical reaction, the invention realizes remarkable purifying effect to SO2 and nitrogen oxides in smoke and gas by the microwave inducing coupling catalysis, the desulfuration and denitration rate can reach above 90 per cent and 85 per cent respectively. The catalyst has simple technique of preparation, good adsorption performance and long service life, which has good catalyst, desulfuration and denitration activity in microwave field.