The structure of Nb-doped anatase TiO₂ (TNO) was calculated using density functional theory (DFT) -based first-principle method. In order to clarify the role of oxygen vacancies, periodic unit cells with several combinations of dopant atoms and oxygen vacancies were investigated. The same calculation scheme was adapted to W-doped anatase TiO₂ (TWO), and Nb-doped rutile TiO₂ for a comparison. The results showed that the possibility of three-body complex in TNO is rather small, compared to the case of TWO and Nb-doped rutile TiO₂. In the latter cases, a strong energy stabilization was observed in a linear W-V_O-W and a bent V_O-Nb-V_O structure, respectively. Feasibility of sufficient sampling of the two-body and three-body interactions was pointed out, and a computational strategy for the assessment of thermodynamical stabilities of the three-body complexes and the chemical potential of oxygen atoms were discussed.