We present the results of a wide-field spectroscopic survey of globular clusters (GCs) in the Virgo cluster. We obtain spectra for 201 GCs and 55 ultracompact dwarfs (UCDs) using Hectospec on the Multiple-Mirror Telescope and derive their radial velocities. We identify 46 genuine intracluster GCs (IGCs), not associated with any Virgo galaxies, using the 3D GMM test on the spatial and radial velocity distribution. They are located at a projected distance 200kpc<~R<~500kpc from the center of M87. The radial velocity distribution of these IGCs shows two peaks, one at v_r_=1023km/s, associated with the Virgo main body, and another at v_r_=36km/s, associated with the infalling structure. The velocity dispersion of the IGCs in the Virgo main body is {sigma}_GC_~314km/s, which is smoothly connected to the velocity dispersion profile of M87 GCs but is much lower than that of dwarf galaxies in the same survey field, {sigma}_dwarf_~608km/s. The UCDs are more centrally concentrated on massive galaxies-M87, M86, and M84. The radial velocity dispersion of the UCD system is much smaller than that of dwarf galaxies. Our results confirm the large-scale distribution of Virgo IGCs indicated by previous photometric surveys. The color distribution of the confirmed IGCs shows a bimodality similar to that of M87 GCs. This indicates that most IGCs are stripped off dwarf galaxies and some off massive galaxies in the Virgo.