We propose insulating titanium oxynitrides TinN2O2n-3 as promising water-splitting photocatalytic materials in the visible light range. Using first-principles many-body perturbation theory based on the GW approximation, we show that corundum-type Ti2N2O (an example TinN2O2n-3 compound with n=2) has a smaller band gap of about 2.5 eV, which is more suitable to absorb visible light, compared to other Ti-based oxides such as TiO2 and SrTiO3 with a band gap of more than 3 eV. Band-gap reduction in Ti2N2O is caused by an upward shift of the valence band (negative shift to the oxidation potential of H2O to O2) due to the presence of nitrogen 2p states. The conduction band is dominated by Ti 3d states and the conduction-band minimum is nearly unchanged. As a result, the band-edge potentials of Ti2N2O are better aligned to the water reduction and oxidation levels. Our theoretical predictions provide useful insights for the discovery of efficient visible-light-driven photocatalysts for water splitting.