•The electronic structures have been altered by the newly formed CNM bonds and the relaxed chemical bonds around them.•The optical absorption edge (and intensity) in visible-light range red-shifts 10–75nm (and increases about 14%–71%) except O– and S– doped specimens.•The separation of the HOMO and LUMO of H–, B–, O–, S–, F– and As– doped specimens can effectively enhance the photocatalytic efficiency.The electronic structures have been altered by the newly formed CNM bonds and the relaxed chemical bonds around them.•The optical absorption edge (and intensity) in visible-light range red-shifts 10–75nm (and increases about 14%–71%) except O– and S– doped specimens.•The separation of the HOMO and LUMO of H–, B–, O–, S–, F– and As– doped specimens can effectively enhance the photocatalytic efficiency. Doping is an effective means to alter the electronic behavior of materials by forming new chemical bond and relaxing the surrounding chemical bonds. With the aid of first-principle studies, the effects of a series of nonmetal (NM) dopants on the geometric, thermodynamic, electronic and optical performances of monolayer g–C3N4 have been investigated. Results shown that, all considered NM atoms except Br and I atoms can be introduced into the monolayer g–C3N4 on account of the thermal stability, the supercell parameter and film thickness have been altered by the newly formed CNM bonds and the relaxed chemical bonds around them, which have affected their electronic structure. The band gap values were altered less than ±0.14eV. The optical absorption edge (and intensity) in visible light of all doped specimens red-shift 10–75nm (and increase about 14%–71%) except for O– and S–doped specimens, and thus the NM dopants can enhance the visible-light response capability. Moreover, the highest occupied molecular orbital and lowest unoccupied molecular orbital of H–, B–, O–, S–, F– and As–doped specimens have been separated adequately, it can effectively separate the photogenerated e−/h+ pairs and enhance the photocatalytic efficiency. Finally, we have confirmed six high efficiency monolayer g–C3N4 based photocatalysts by doping H, B, O, S, F and As atoms.