基于夫琅禾费衍射理论，通过对衍射积分的核函数进行近似，推导并得出了简洁的经圆环形孔径衍射的高斯光束远场发散角的近似解析式。在不同衍射孔径外径和不同遮拦比的条件下，将该解析式与严格的夫琅禾费衍射积分进行比较，发现二者求出的远场发散角接近一致，最大误差不超过2.7%。与传统数值积分求取光束发散角相比，该近似解析式在避免繁琐的积分运算同时保持了较高的精度。该解析式成立条件为高斯光束的束腰直径大于等于3.5倍中心遮拦直径，且小于等于孔径直径；在实际工程应用中，特别是具有大口径、小遮拦比特点的空间激光通信光学天线这一应用场景，该条件一般能够被满足。

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.