We employed tight-binding calculations and Green’s  function formalism to investigate the effect of applied electric fields on the energy band and electronic properties of bilayer  armchair graphene nanoribbons  (BL-AGNRs). The results show that the perpendicular electric field has a strong impact on modifying and controlling the bandgap of BL -AGNRs.  At the critical values of this electric field, distortions of energy dispersion in subbands and the formation of new electronic excitation channels occur strongly. These originate from low -lying energies near the Fermi level and move away from the zero -point with the increment of  the electric field. Phase transitions and structural changes clearly happen in these materials. The influence  of the parallel electric field is less important in changing the gap size, resulting  in the absence of the critical voltage over a very wide range [ –1.5 V; 1.5 V] for the

semiconductor-insulator group. Nevertheless, it is interesting to note the powerful role of the  parallel electric field in modifying the energy band and electronic distribution at each energy  level. These results contribute to an overall picture of the physics model and electronic  structure of BL-AGNRs under stimuli, which can be a pathway to real applications in the  future, particularly for electronic devices.