Abstract: On the basis of the extended Huygens-Fresnel principle, the cross-spectral density matrix (CSDM) of partially coherent Gaussian-Schell model (GSM) beams propagating in atmospheric turbulence is derived. Given that the light emitted from a transmitter is elliptically polarized light, the degree of polarization (DoP) of beams is represented by Stokes parameters expressed by the elements of the CSDM. The expression of the degree of ellipticity is derived. Depolarization theory is studied using a Mueller matrix and the depolarization index (DI) is obtained to describe the depolarized state of beams propagating in the slant atmospheric turbulence. Numerical results show that the factors of the wavelength of beam, source coherence length, light spot size, propagation distance and turbulence level will have impact on the DoP, degree of ellipticity and DI. This study may provide theoretical basis for future applications in the atmospheric optical communication field.