The simple approximated analytic expression for the far-field divergence angle of Gaussian beam diffracted by an annular aperture was derived based on the Fraunhofer diffraction theory and by the approximate of the diffraction integration kernel function. For diffraction aperture with different diameters and obscuration ratios (OR), the analytic expression was compared by strict Fraunhofer diffraction expression, and the far-field divergences solved by these two expressions were nearly identical. The error was no more than 2.7%. Compared with the traditional method of getting the beam divergence by numerical integration, the troublesome integral was avoided, but a relative high precision was kept through this approximated formula. The analytic formula was effective on condition that the Gaussian beam waist diameter was more than or equal to 3.5 times the obscuration diameter, and less than or equal to the aperture diameter. In an actual engineering application, especially the space laser communication optical antenna with the characteristics of large-aperture and small-OR, the establishing conditions generally are satisfied.