Based on the phase modulation of axicons and the amplitude modulation of films, an exactly and high-efficiency generation scheme of non-diffractive Mathieu beams is proposed. With the stationary-phase technique, the theoretical mechanism of the generation of Mathieu beam by this scheme is verified. The amplitude modulation film with an angular Mathieu function is prepared by the usage of the film recorders, and a family of Mathieu beams is experimentally generated. The theoretical and experimental results show that the proposed method for generating Mathieu beams based on axicons and the amplitude modulation is simple, flexible and highly efficient.