Based on first-principles calculations, we have investigated the structural and electronic properties of AMoSe2NRs with different edge functionalization. We have considered two patterns of edge passivation for AMoSe2NRs: one is simplex edge passivation and the other is hybrid edge passivation. In addition, different functionalization groups are taken into consideration. The results show that all these passivated strategies can be used to stabilize the pristine system, especially the hybrid passivation ones, and the pristine and edge functionalized nanoribbons are nonmagnetic semiconductors with the tunable band gaps varying in a range 0–1.19 eV and along with a gradient of near 0.1 eV. The O-functionalized nanoribbon is a nonmagnetic metal, however, when pristine nanoribbon is passivated by hybrid oxygen and hydrogen atoms, it returns to the nonmagnetic semiconductor. It is exciting to find that the electronegativity of passivated atom plays an important role in engineering the band gap of pristine AMoSe2NRs.