A wet ammonium flue gas cleaning process for desulfurizing and denitrifying and a system thereof are disclosed. The process oxidates NO in the flue gas to be NO2, makes SO2 and NO2 in the flue gas react with ammonium to product ammonium sulfite, ammonium nitrate and ammonium nitrite, then oxidates ammonium sulfite and ammonium nitrite therein to product the byproduct that is ammiaonia sulfate and ammonium nitrate, and lastly gets the clear flue gas after demisting to the desulfurizing and denitrifying flue gas. The system comprises a dust pre-collector, a hydrogen peroxide or ozone sprayer, and a desulfurizing and denitrifying tower, which are connected in turns, wherein ammonia replenishment system and an air feeding device are mounted at the bottom of the desulfurizing and denitrifying tower, sprinkling layer which can cycle sprinkle is mounted at the middle, and a demister is mounted at the upper. The invention has a simple process, a simplified system, a low investment and operation cost. The invention not only has a high efficiency in desulfurizing and denitrifying, but also a high utilance of desulfurizing and denitrifying absorbent, and byproduct of desulfurization and denitration can be utilized as chemical fertilizer of ammiaonia sulfate and ammonium nitrate.