The beam transmission characteristics of elliptical aperture and axicon system are studied based on the Fresnel diffraction theory, complex Gaussian function expansion and stationary phase method of hard-edged aperture. The formula of non-diffracting optical fields after Gauss plane wave propagating through the axicon is deduced, the transverse intensity distributions of the beam in different propagation distances are numerical simulated and the experimental verification is also carried out. The intensity distributions in different propagation distances are captured by a charge coupled device (CCD) camera. The experimental results and numerical simulation all suggest that plane wave passing through a optical system with an elliptical aperture and axicon can obtain the qausi-non-diffracting beam which has similar characteristics to Mathieu beam. This result has guiding function in the application of optical nondestructive testing and barcode scanning.