Based on the extended Huygens-Fresnel principle,taking the random el ectromagnetic ShG beam as a typical example of random electromagnetic beams,the analytical expressions of t he cross-spectral density matrix elements for random electromagnetic ShG beam propagating in atmospheric t urbulence are derived,and used to study the changes in on-axis degree of polarization P,orientation angle θ,and ellipticity ε of random electromagnetic ShG beams in atmospheric turbulence.It is shown that the change s in on-axis degree of polarization P,orientation angle θ,and ellipticity C²_n d epend on the structure constant ,the Sh-part parameter Ω₀,the spatial correlation length,and the propagation distance z of random electromagnetic ShG beams in atmospheric turbulence.The decrement of structure constant C² n,as well as the increment of the Sh-part parameter Ω₀,the transition position of orientation a ngle θ.will increase,and the distance for minimum degre e of polarization P and maximum ellipticity ε will increase.As for the longger distance,the Sh-part parameter Ω_0h as no effect on the degree of polarization P,orientation an gle θ and ellipticity ε.The w ork will provide the theoretical foundation and experimental basis for analyzing the states of polari zation of random electromagnetic beams in free space optical communications.