The Nb-doped anatase TiO2 is considered one of the most promising alternative transparent conducting oxides to substitute for indium tin oxide. However, studies have found that the conductivity emerges only in the anatase form, not in the rutile form. We applied the first-principle band structure method for the Nb-doped TiO2 in both polymorphs. The calculation was carried out using the spin-restricted and spin-polarized GGA+U level of the theory. Special care was taken in the calibration of +U parameters to satisfy the generalized Koopman's theorem. A significant difference was found between the spin-polarized and spin-restricted calculations. We noticed that spin polarization was necessary to reproduce the electron trapping in rutile. In addition, electrons are trapped at two lattice Ti atoms adjacent to the Nb-Ti dopant along the [001] direction, as described with the formal charge state of Ti3.5+-Nb5+-Ti3.5+. A careful convergence of the electron trapping character was conducted against the unit cell size based on the Bader population analysis.