Nondiffracting Bessel, Mathieu, and Weber vector beams are generated by using ring-shaped plasmonic geometric metasurfaces. The nondiffracting vector beam is produced by the superposition of two off-axis right-handed and left-handed circularly polarized nondiffracting scalar beams described by the Whittaker integral, which are simultaneously generated by a single metasurface with the ring-shaped phase profile. The polarization states of the generated nondiffracting vector beams are analyzed by the Stokes parameters and the orbital angular momentum states are measured by the beam interference. In addition, the selfhealing properties of nondiffracting vector beams are further demonstrated, showing that not only the beam profiles but also the polarization states can be recovered behind the small opaque obstacle. The demonstrated ring-shaped plasmonic metasurfaces provide a compact and efficient platform to produce complex nondiffracting vector beams and pave the way to many promising applications related to spin and orbital angular momentum conversion, quantum information processing, optical manipulation, and optical communication.