By the aid of using Gaussian function instead of Bessel function in the Fraunhofer diffraction formula,the simple approximated analytic expression for the far-field divergence angle of Gaussian beam diffracted by a circular-aperture collimation optical system was obtained. For different diffraction conditions,the expression was compared by strict Fraunhofer diffraction expression,and the far-field divergences solved by these two expressions were nearly identical. With the same diffraction aperture,the error between approximated analytic solution and true value is reduced with the increase of the initial beam wrist;with the same initial beam wrist,the error increases slightly with the rise of the diffraction aperture semi-diameter,and finally flatten out. On condition that the intial waist is not less than 2 μm,the maximum of the error is no more than 3.4%. Therefore the approximated analytic expression correctly describes far-field diffraction divergence in every diffraction case,and has handy form. At the same time,through the comparision for the beam divergence in different diffraction aperture diameters and initial beam wrists,it can be seen that the beam divergence decreases with the increasing of the circular aperture semi-diameter and increases with the increasing of initial wrist.