Based on the extended Huygens-Fresnel principle, the propagation properties of electromagnetic Gaussian multi-Schell model beams through atmospheric turbulence in a slanted path are investigated in detail. Results indicate that the changing of transverse coherence length has an effect on the far-field intensity distribution and the beam width induced by atmospheric turbulence of the laser beam. Besides, the degree of polarization of the electromagnetic Gaussian multi-Schell model beams can change with the propagation distance, and it can reach a certain value when the laser beam propagates through atmospheric turbulence in a slant path. This result indicates potential applications for satellite-to-ground or ground-to-satellite laser communications.