A series of chiral anatase (101) nanotubes (NT), which we refer to as (*n*,0), (0,*m*), and (*n,m*), can be formed by rolling up two-dimensional periodic anatase TiO_{2} (101) single layer sheets. Optimized parameters of the atomic and electronic structures of these nanotubes have been calculated using a tight-binding density functional theory method (DFTB). Their band gaps (*E*_{g}) and strain energies (*E*_{s}) have been analyzed as functions of NT diameter. Except for (6,0), the strain energy and the band gap of all the nanotubes of various chirality decrease as the diameter increases. We also find that the strain energy increases first and then decreases rather than varying monotonically with almost constant band gap when *n/m* ranges from zero to infinitely large.