Abstract: The distribution of the optical field generated by focusing an astigmatic elliptical Gauss beam using an axicon is studied and the formula of the optical field diffracted by the axicon is derived from Fresnel diffraction integral theory. The intensity of the optical field distribution is calculated by numerical integration. Comparing the field intensity generated by elliptical Gauss beam with the field intensity generated by impinging circular Gauss beam on an axicon, we find that the beam generated by an astigmatic elliptical Gauss beam also has the interesting property of non-diffraction in a certain propagation distance and the similar distribution of on-axis intensity of Bessel-Gauss beam generated by circular Gauss beam, however, the intensity of the optical field perpendicular to optical axis is not cylindrically symmetrical. The maximum non-diffracting lengths of elliptical Bessel-Gauss beam on meridional and sagittal planes are also calculated according to the maximum non-diffractive length formula of spherical wave generating quasi-Bessel beam, and the non-diffracting length of the whole beam is limited by the size of minor axis of incident elliptical spot on the axicon.