Non-classical polarization properties of the two-mode partially coherent Gauss-Shell model beam propagating through non-Kolmogorov turbulence are analysed. The analytic equation for the polarization degree of the quantum state of the two-mode light field is obtained. Results show that the polarization fluctuations of the quantum state of the two-mode light field are dependent on the turbulence and the detection photon numbers. The polarization degree of the quantum state of the two-mode field gradually decrease. Furthermore, the bigger difference is on the two orthogonal polarization modes detected photon numbers, the better the polarization properties of the two-mode light field are maintained, which is contrary to the two-mode coherent state light field.