The lateral and on-axis diffractive intensity distributions of an axicon lens illuminated by the monochromatic and quasi-monochromatic Gaussian beams are numerically calculated and discussed by using the angular spectrum method. Also, the on-axis diffractive intensity distribution of the axicon illuminated by uniform monochromatic plane wave is given. Unlike the well-known Fresnel diffraction integral, the propagation theory of angular spectrum defers to the more rigorous Helmholtz scalar wave equation with fewer approximation, resulting in more accurate results. The results of numerical calculation show that the intensity distribution of diffractive field in the rhombic region determined by the overlap of light rays has the characteristics of diffraction-free Bessel beam. The intensity on the optical axis changes in a fluctuating way which shows direct correlations with the lateral intensity distribution of the incident waves. In the quasi-monochromatic case, the contrast of Bessel fringes and the degree of fluctuation of on-axis intensity tends to decrease slightly, depending on the bandwidth of incident beam, while the intensity distribution keeps the same form as the monochromatic case.