Based on the unified theory of coherence and polarization of random electromagnetic beams and the propagation law of cross-spectral density matrix,the closed-form expression for the 2×2 cross-spectral density matrix of random cosh-Gaussian(ChG) electromagnetic beams propagating through a lens is derived,and used to formulate the degrees of cross-polarization,i.e.,the longitudinal degree of cross-polarization (LDCP) and the transverse degrees of the cross-polarization (TDCP) between two arbitrary points upon propagation. It is shown that the degrees ofcross-polarization depend on the focal length of the lens and beam parameters,such as the coefficient ratio,decentered parameter and self-correlation length. The degrees of cross-polarization of radom Gaussion Schell-model (GSM) electromagnetic beams propagating through a lens can be treated as a special case that the decentered parameter of random ChG electromagnetic beams approaches to zero. The main results are illustrated numerically and interpreted physically.