Crystal structure, electronic properties, and stability of anatase and rutile Nb-doped TiO2 (Nb:TiO2) compounds with different doping concentrations are studied by the combination of GGA and GGA+U methods within the density functional theory based first-principle calculation. And the main research work and contents are listed as follows: The anatase Nb:TiO2 appears as a degenerated semiconductor which behaves as an intrinsic metal. Its metallic property arises from Nb substitution into the Ti site, providing electrons to the conduction band. In contrast, the rutile Nb:TiO2 shows insulating behaviors. Ionization efficiency of Nb in anatase Nb:TiO2 is higher than that in rutile. We expect that anatase Nb:TiO2 is a potential material for transparent conducting oxide (TCO) while rutile Nb:TiO2 is not. The doped systems show different electronic characteristics, such as band structure, Fermi energy, and effective mass of carriers at different doping levels. In higher dopant concentration nNb, the ionization efficiency decreases slightly. Calculated defect-formation energy shows that Ti-rich material growth conditions are not in favor of the introduction of Nb while Nb can be easily doped in Nb:TiO2 under O-rich growth conditions. Nb dopant is difficult to be doped at higher doping level for both anatase and rutile Nb:TiO2.