Stacked and single-layered lepidocrocite-type titanium dioxides (hereafter denoted as single-layered and stacked TiO2's, respectively) have been investigated by using first-principles calculations within density functional theory. The crystal structures, electronic structures, dielectric properties, and mechanical properties have been studied. The validity of the present theory was confirmed by reproducing the experimental properties of known bulk TiO2 polymorphs (rutile and anatase). As for a single-layered lepidocrocite-type TiO2, the optimized structural parameters agree well with the reported data of an exfoliated nanosheet of Ti0.91O2 or Cs(0.7)Ti(1.825)O(4)rectangle(0.175) (rectangle = vacancy). Single-layered TiO2 is slightly less stable than rutile and anatase. The band gap of single-layered TiO2 is 3.15 eV, which is larger than those of rutile and anatase due to a quantum size effect in a two-dimensional structure with a thickness less than 1 nm. The dielectric constant of the single-layered lepidocrocite-type TiO2 is highly anisotropic. The elastic constant of single-layered TiO2 shows an extra flexibility along the sheet normal.