The characteristics of two noninteger cylindrical vector vortex beams (NCVVBs) propagating through a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The NCVVBs exhibit periodic and stable transmission characteristics in the radial GRIN fiber. Polarization changes, the presence of spin angular momentum (SAM), and changes in the orbital angular momentum (OAM) of the NCVVBs are observed at the focal plane of the radial GRIN fiber. Spin-orbit interactions of NCVVBs are verified in the radial GRIN fiber for the first time, to the best of our knowledge.