Based on the generalized Huygens-Fresnel principle and the theory of c oherence and polarization of light,it was derived that the analytical expression of the cross spectral de nsity matrix element of random electromagnetic Gaussian vortex beam in gradient-index fiber,the spectral degr ee 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 i n 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 distributio n of the spectral degree of coherence is the same as the topological charge m.The value of spatial correlat ion length σ_xx change the evolutive speed of the spectral degree of coherence along the radial direction, while spatial correlation length σ_xy dose not change the distribution of th e spectral degree of coherence.The research results of this paper have guiding significance for the propagation of random electromagnetic vo rtex beams in optical fibers,and have reference value in high-speed and large-capacity optical fibe r secure communication.