In this paper we present new results obtained from our spectroscopic survey of near-Earth objects (called SINEO). We show a set of 36 visible and near-infrared spectra, recorded with the 3.5-m Italian Telescopio Nazionale Galileo at La Palma (Canary Island). We discuss their taxonomic classification (resulting in 25 objects belonging to the S-complex, five to the C-complex and six to the X-complex), and their overall compositional linkage with the principal source of near-Earth objects, namely the Main Belt. Moreover, for some near-Earth objects we found good spectral fit among meteorites. In particular, we achieved an excellent fit for chondrites of different clans. Finally, we discuss the influences of space weathering among small S-type near-Earth objects.