To investigate the relationship between the electronic structure and the power factor of Nax CoO2 (x =0.3,0.5 and 1.0),the first-principles calculation is conducted by using density functional theory and the semi-classical Boltzmann theory.Our results suggest that with the decreasing Na content,a transition from semiconductor to semimetal is observed.Nao.3CoO2 possesses a higher electrical conductivity at 1000 K due to its increased density of states near the Fermi energy level.However,an optimal Seebeck coefficient at 1000 K is obtained in Nao.sCoO2 because of its broadened band gap near the Fermi energy level.Consequently,a maximum power factor is realized in Nao.sCoO2.Thus our work provides a complete understanding of the relationship between the electronic structure and the thermoelectric power factor of Nax CoO2.