The characteristics of the cylindrical vector beam (CVB) and the cylindrical vector vortex beam (CVVB) in a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The CVB and CVVB exhibit periodic and stable transmission characteristics in the radial GRIN fiber. In the beam with a vortex phase (CVVB), the polarization changes and the spin angular momentum (SAM) is detected at the focal plane of the radial GRIN fiber. A spin-orbit periodic conversion is observed in the radial GRIN fibers. Finally, the SAM expression of partially coherent light is deduced and verified via a simulation.