A class of annular light beams with flat-topped Gaussian profile (i.e., Gaussian doughnut mode) is introduced. Field distribution of this kind of beams can be obtained by subtracting from a flat-topped Gaussian function [Proc. of SPIE, 5525, 128-137 (2004)] with another flat-topped Gaussian function of different width. The proposed expression can be easily expanded into a series containing the lowest order Gaussian modes of different waist parameters. This situation significantly improves the numerical calculation efficiency in the investigation of propagation properties of annular beams and also provides the possibility to investigate the aperture effect that a beam may be experienced when the beam passes progressively from smooth Gaussian aperture toward the hardedge limit. Results are illustrated by examples and compared with the prediction of Lommel theory of diffraction of plane waves at an annular aperture.