The cross-spectral density function of stochastic electromagnetic vortex beams in non-Kolmogorov turbulent atmosphere is presented on the basis of the unified theory of coherence and polarization, and the analytic expressions of the intensity and the degree of polarization of on-axis point are derived. It is shown that the evolution of intensity and polarization of vortex beams in atmosphere is different from that of non-vortex beams, and is influenced by the correlation length and the topological charge of the incident vortex beams. Some important results are concluded and discussed.