Based on the theory for the irradiance fluctuations (scintillation) of the spherical wave propagating in the turbulent atmosphere and the annular-aperture filtering function, the expression of annular-aperture averaging factor was obtained. The annular-aperture averaging factor was fitted into a second-order polynomial about a dimensionless parameter, i.e. the ratio of the aperture radius to the Fresnel size. After establishing the relationship between the polynomial coefficients and the ratio of the inner to outer diameter of the aperture, the annular aperture averaging factor is expressed approximately as a function of this dimensionless parameter and the ratio of the inner to outer diameter of the aperture. The valid range and accuracy of the fitted approximation were evaluated by error analysis. The effect of the turbulent inner scale on the annular-aperture averaging factor was also analyzed by using Tatarskii spectrum and modified Hill spectrum. The results reveal that, when other conditions keep invariable, the larger the inner scale is, the weaker the averaging effect of the annular aperture is.