The effects of strong interactions between Ti and ceria on the structures of Ti/CeO2(111) are systematically investigated by density functional theory calculation. To our best knowledge, the adsorption energy of a Ti atom at the hollow site of CeO2 is the highest value (-7.99 eV) reported in the literature compared with those of Au (-0.88--1.26 eV), Ag (-1.42 eV), Cu (-2.69 eV), Pd (-1.75 eV), Pt (-2.62 eV) and Sn (-3.68 eV). It is very interesting to find that Ti adatoms disperse at the hollow site of CeO2(111) to form surface TiOx species, instead of aggregating to form Ti metal clusters for the Ti-CeO2 interactions that are much stronger than those of Ti-Ti ones. Ti adatoms are completely oxidized to Ti4+ ions if they are monatomically dispersed on the next near hollow sites of CeO2(111) (xTi-NN-hollow); while Ti3+ ions are observed when they locate at the near hollow sites (xTi-N-hollow). Due to the electronic repulsive effects among Ti3+ ions, the adsorption energies of xTi-N-hollow are slightly weaker than those of xTi-NN-hollow. Simultaneously, the existence of unstable Ti3+ ions on xTi-N-hollow also leads to the restructuring of xTi-N-hollow by surface O atoms of ceria transferring to the top of Ti3+ ions, or oxidation by O2 adsorption and dissociation. Both processes improve the stability of the xTi/CeO2 system by Ti3+ oxidation. Correspondingly, surface TiO2-like species form. This work sheds light into the structures of metal/CeO2 catalysts with strong interactions between the metal and the ceria support.