Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary phase method, within the maximum non-diffraction distance behind an axieon,the optical field distribution of a nanosecond Gaussian beam pulse pass ing through axieons with the ideal manufacture quality and with the elliptical manufacture error were investigated. According to the derived field expression, the three-dimensional intensity distributions and corresponding beam patterns were simulated numerically. It is shown that the different elliptical manufacture error,the propagation distance and the beam Wavelength had an effect on the propagation of the nanosecond Bessel beam pulse in the presence of an elliptical manufacture error in the axcion. The film-scan method was adopted to record the nanosecond beam patterns in the transverse plane which perpendicular to the propagation axis. The experimental results fit the theoretical simulations well.