The invention belongs to the technical field of atmospheric pollution control, and specifically discloses a catalyst for cooperative control of multiple pollutants in waste incineration flue gas and a preparation method and application of the catalyst. An M/MgAl-LDH catalyst containing Co and Ce is synthesized through a coprecipitation method. A Mg-Al hydrotalcite material is firstly synthesized, then Co and Ce are loaded through a coprecipitation method, and finally the obtained product is dried and subjected to high-temperature calcination to obtain a composite metal oxide catalyst, which is used for studying catalytic oxidation for cooperative control of multiple pollutants in waste incineration flue gas. The catalyst has the NOx purification efficiency higher than 85%, the SO2 purification efficiency higher than 90%, and can remove about 95% of HgO from waste incineration flue gas in the presence of little HCl at a low air speed. Compared with combination of single pollutant control technology, the catalyst can purify multiple pollutants, and the investment cost and operation cost can be effectively reduced.