The electronic properties of quasi-one-dimensional anatase TiO2 nanostructures, in the form of thin nanowires having (101) and (001) facets, have been systematically investigated using the standard, hybrid density functional and quasiparticle calculations. Their visible photoabsorption characteristics have also been studied at these levels of theories. The thin stoichiometric nanowire models are predicted to have larger band gaps relative to their bulk values. The band-gap-related features appear to be better described with the screened Coulomb hybrid density functional method compared to the standard exchange-correlation schemes. Depending on the self-consistency in the perturbative GW methods, even larger energy corrections have been obtained for the band gaps of both (101) and (001) titanium dioxide nanowires. © 2014 American Physical Society.