We have numerically investigated the supercontinuum generation by a femtosecond annular Gaussian beam in air. Compared with the spectra broadening of the Gaussian filament under the same initial condition, the smooth supercontinuum spectra of the annular Gaussian filament are wide enough to cover the whole visible frequency range in the first focusing cycle. The spectra broadening is analyzed from the frequency shift induced by the ionization and the self-phase modulation. For the blue side of the enhancement of the spectra broadening, the ionization-induced and intensity-induced frequency shifts play the dominant role in the onset distance of the filament and the first maximum value of the spectra broadening, respectively. Then, we have also discussed the influences of the initial pulse energy and the spatial chirp for wide and smooth supercontinuum spectra to cover the whole visible frequency range. Therefore, it is an efficient route to produce the supercontinuum spectra by the annular Gaussian beam.