Based on the generalized Huygens-Fresnel principle and the theory of coherence and polarization of light,it was derived that the analytical expression of the cross spectral density matrix element of random electromagnetic Gaussian vortex beam in gradient-index fiber,the spectral degree of coherence of the random electromagnetic Gaussian vortex beam propagating through gradient-index fiber is studied.The results show that when random electromagnetic Gaussian vortex beam propagating in gradient-index fiber,the period of the spectral degree of coherence is related to the gradient-index coefficient β.the longer beam wavelength is,the more obvious the focusing effect of the gradient-index fiber on the distribution of the spectral degree of coherence is.The number of dark rings in the distribution of the spectral degree of coherence is the same as the topological charge m.The value of spatial correlation length σxx change the evolutive speed of the spectral degree of coherence along the radial direction,while spatial correlation length σxy dose not change the distribution of the spectral degree of coherence.The research results of this paper have guiding significance for the propagation of random electromagnetic vortex beams in optical fibers,and have reference value in high-speed and large-capacity optical fiber secure communication.