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In this paper, the manipulative effect of N doping on topological insulator Bi 2 Se 3 was investigated by using density functional theory (DFT). The computational results reveal that the van der Waals (vdW) correction is necessary when calculating the geometric structure of Bi 2 Se 3. Taking into account the spin–orbit coupling(SOC), the electronic structure of Bi 2 Se 3 can be accurately described, especially for the energy bands near the Fermi level. The N doping at anion sites can produce an impurity band which appeared at Fermi energy. Comparing with pure Bi 2 Se 3 , the electronic structure of N doping Bi 2 Se 3 changed obviously at Fermi energy. The valence band and conduction band meet when N doped on Se1 sites, the insulating properties of Bi 2 Se 3 system are damaged. The indirect gaps between the valence band and conduction band are 0.135 eV and 0.115 eV with N doping on Se2 sites with the doping levels 6.67% and 1.67%, respectively. On the other hand, the N doping at Se sites of Bi 2 Se 3 can induce magnetic moments. The magnetic moments are related to the covalent bond length between N atom and Bi atom. Furthermore, the real and imaginary parts of dielectric functions have been computed. The static dielectric constant ε 1 (0) becomes significantly larger and the peaks in the imaginary part of dielectric constant ε 2 (ω) spectra move toward low energy. The intensity of the peak is gradually enhanced and there is a small bump in Bi 6 Se 8 N2 at 0.38 eV. The N doping paves a prospective way to tune the topological properties and may find change to potential spintronic applications and electronic devices. • The electronic structure of N doping Bi 2 Se 3 are changed obvious at fermi energy. • The insulation properties of Bi 2 Se 3 system are damaged with N doping on Se1 sites. • The N doping at Se sites can induce magnetic moments. [ABSTRACT FROM AUTHOR]