Based on the extend Huygens-Fresnel principle,the analytical expressions for cross-spectral density matrix elements of random electromagnetic Sinh-Gaussian (ShG) beams as typical stochastic electromagnetic beams propagating through atmospheric turbulence are derived,and used to study change in the transverse degree of polarization of random electromagnetic ShG beams propagating in atmospheric turbulence.It is shown that distribution of transverse degree of polarization varies with location when random electromagnetic ShG is propagating in atmospheric turbulence.The smaller the structure constant C2 n ,the larger the Sh-part parameter Ω0 ,or the bigger the spatial correlation length σxy (σyx ) ,the longer the propagation distance of distribution of polarization into bimodal shape,flat shape,unimodal shape.