The invention discloses a device for removing a composite pollutant, which comprises a removing tower. A flue gas inlet is arranged at the lower part of the removing tower; a flue gas outlet is arranged at the upper part of the removing tower; at least one layer of sprayer is arranged in the removing tower at the upper part of the flue gas inlet; and a wet electrical dust precipitator is also arranged in the removing tower above the sprayer. The method for removing the composite pollutant sequentially comprises the steps of spraying and absorbing and wet electrical dust removing. The invention has the advantages that a demister in an FGD (Flue Gas Desulfurization) device is omitted; the removal rate of SO2 in flue gas can be ensured to reach more than or equal to 96 percent; the removal rate of mercury can be ensured to reach more than or equal to 75 percent; the removal rate of acid mist aerosol can be ensured to reach more than or equal to 95 percent; the removal rate of PM2.5/PM10 can be ensured to reach more than or equal to 95 percent; and by using an SCR (Selective Catalyctic Reduction) process for denitration or an ammonia method process for desulfurization, the ammonia escape can be controlled below 5ppm.