Based on Fresnel diffraction theory and complex Gaussian function expansion of hard-edged aperture, the optical field formula of Bessel beam propagating through an elliptical annular aperture is derived, and the transverse intensity distribution of the beam is numerically simulated. The changes of the optical field and the propagation process of the diffracted beam behind the elliptical annular aperture are studied. In the experiment for the first time, a quasi non-diffracting beam is generated by an axicon and the patterns that are due to the beam diffraction by an elliptical annular aperture at different propagation distances are observed with a charge-coupled device camera. The theoretical analysis and experimental results both show that Bessel beam passing through an elliptical annular aperture can generate a hollow beam.