The structure, stability, Youngs modulus and electronic band structures of lepidocrocite-type and anatase-type TiO2 nanotubes were investigated using density functional theory calculation. It was found that the anatase-type nanotubes were energetically more favorable than lepidocrocite-type nanotubes when the diameter of nanotube is small, whereas the lepidocrocite-type nanotubes were energetically more favorable when the diameter of nanotube was large. Youngs modulus of TiO2 nanotubes is calculated. The results obtained show that all TiO2 nanotubes have relatively good mechanical properties, and lepidocrocite nanotubes are stronger than anatase nanotubes. Interestingly, it was found that the electronic band structures of TiO2 nanotubes are influenced by the tubular chirality. Lepidocrocite （0, n） and anatase （n, 0） nanotubes are of indirect band gap type, whereas lepidocroctie （n, 0） and anatase （0, n） nanotubes have direct band gaps.