The absorption spectra of cobalt-doped anatase TiO_2 nanopowders in the infrared and visible ranges have been studied after various oxidative and reductive treatments. The annealing leads to the appearance of the Drude-like contribution in the infrared region and significant change in the absorption in an visible range due to the formation of defects of the oxygen-vacancy-type and Ti^3+ ions. The observed additional contribution in the absorption spectra of TiO_2:Co nanopowders as compared to the spectra of undoped powders is ascribed to the d – d transitions in ions Co^2+. The change in the absorption related to cobalt after annealing is explained by a change in the local environment of Co ions from the octahedral to the tetrahedral environment.