With the help of the unified theory and polarization of partially coherent beams, and the propagation law of the 2×2 cross\|spectral density matrix, the general formula was derived to calculate the degree of polarization for a class of stochastic electromagnetic vortex beam transmitted through a circular ring. Based on these theories, the changes of degree of polarization of the Laguerre\|Gaussian beam and its propagation characterization have been investigated. It is shown that the degree of polarization will change after the beam transmitted through the circular ring, and the degree of polarization of the diffractive beam is related with the coherence, the topological charges of the source, and the size of the circular ring.