The invention discloses an anion exchange membrane for a fuel cell, a preparation method of the anion exchange membrane for the fuel cell, and the fuel cell applying the anion exchange membrane. The preparation method of the anion exchange membrane comprises the steps of mixing polymeric ionic liquid, a polymeric monomer A and an emulsifying agent, dripping the mixed liquid onto a glass plate, andputting into a radiation field in the nitrogen atmosphere; carrying out radiation for 30-40min by using a cobalt 60-gamma radiation method, and carrying out a polymerized radiation radical reaction;then, soaking the prepared polymer film in 0.5-1mol/L KOH solution for 60-78h at 50-60 DEG C, and carrying out ion exchange; finally, soaking the film in deionized water until the rest deionized wateris neutral. The anion exchange membrane prepared by the method has better alkali resistance, mechanical performance, and higher ionic conductivity and heat stability.