A novel and simple optical element is designed. If beams passing through this diffractive element and focused by a lens, non-diffracting Mathieu beams are realized. Moreover, the q values of Mathieu beams vary with the parameters of diffractive elements. The Mathieu beam expression of this optical system is derived theoretically by discrete Fourier methods and the beam spot intensity is simulated with Matlab. The numerical simulation as well as experimental result confirm the validity of producing non-diffracting Mathieu beams by this diffractive element.