Transition-metal oxides LiTi2O4 thin film was epitaxially grown on MgAl2O4 (001) substrate by pulsed-laser deposition. The X-ray diffraction indicates that the film was successfully grown with high quality and single cubic spinel phase. The Raman-active phonons were studied by Raman spectroscopy. Using spectroscopic ellipsometry, we also determine the refractive index and extinction coefficient of the film in visible-near-infrared region. Band structure and density of states (DOS) of LiTi2O4 were carried out by first-principles calculations. The theoretical calculations are consistent with the experimental results, and the optical constants is well identified by the theoretical band structure.