We study the geometry structures, formation energies, electronic and optical properties of C-anion doped anatase TiO2. We optimize the geometries using planewave pseudopotential density functional and calculate the electronic structures using Heyd-Scuseria-Ernzerhof hybrid functional. The sample has the lowest formation energy when the C-Ti bonding is along certain direction. The carbon doping induces impurity states. Some lead to the narrowed bandgap and increase electron transition efficiency, whereas others result in electron-hole recombination centers. Compared with other theoretical results, ours agree well with the experiments to explain the different optical absorption thresholds. The electronic structures relate to the doping position, but not doping concentration. (C) 2016 Elsevier B.V. All rights reserved.