It is well known that the paraxial approximation is no longer valid for the beams with large divergence angle or small spot size comparable with the wavelength. Thus,a rigorous non-paraxial treatment becomes necessary. For the aperture diffractions,the high-order series expansion corrections are not very good if the propagation distance z is relatively long,because contributions due to the high-frequency components cannot be neglected. Therefore its applicable range is very limited. Based on the scalar diffraction theory of the angular spectrum representation,detailed numerical calculation for the circular aperture diffraction is given,and the non-paraxial corrections to the paraxial solution are derived. It is pointed out that the higher-order non-paraxial corrections are necessary in the near field or in the non-paraxial area. Also,their validity is studied.