It is well known that the scalar approximation is no longer valid for the beams with small spot size comparable with the wavelength. Detailed numerical calculations for the series expansion solution,non-paraxial approximation solution and exact solution of vectorial Gaussian beams diffracted at a small circular aperture are performed and compared;It is shown that the series expansion solution is valid in the near-field region,and the non-paraxial approximation solution is valid in the non-near-field region for the propagation of a nonparaxial beam diffracted by a small hard-edge aperture,and they are compensated mutually.The validity of the scalar approximation of Gaussian beams diffracted at a circular aperture is discussed;the scalar diffraction theory is rigorous and valid when the waist width of a Gaussian beam and the aperture size is larger than several wavelengths.