Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF),the analytical expressions for the beam prop agation factors (M^2factors) and angular spread of Gaussian Schell-model (GSM) vortex beams (topological charge m=±1) and non-vortex beams propagating through atmospheric turbulence and free space are derived,and they a re used to study the influence of atmospheric turbulence parameters and beam parameters on the beam quality.It i s shown that the smaller the propagation distance z,the structure constant C²_n and the spatial correatin length σ₀are,as well as the larger the inner scale l_0and the wavelength λ are,the less the propagation of GSM vortex beams is affected by atmospheric turbulence is,and the better the beam quality is.Compared with the GSM non-vortex beam,the GSM vortex beam is more beneficial to the beam propagation through atmospheric turbu lence and is more conformable to be applied to the atmosphere laser communications.The work can provide th e theoretical foundation and experimental basis for free space optical communications and laser weapon.