[en] Highlights: • We use of the Green's function method and the tight-binding Hamiltonian model. • Using DFT methods we will parametrize the tight-binding hopping and on-site energies. • The electronic properties of graphene/h-BN and h-BN bilayers system are studied. • The electron transport in the GNR/BNNR/GNR structure can open a conduction gap. We use a tight binding approach to study of electron transport properties of bilayers of zig-zag graphene/h-BN nanoribbon (GBNNR) and h-BN nanoribbon (BNNR) embedded between two bilayer of zig-zag graphene nanoribbons (GNR), which are considered as electrodes. In this study, the parameters of tight biding hopping and on-site energies are obtained by comparing the tight binding band structure graphene/h-BN and h-BN bilayers with density functional theory (DFT) calculations. We numerically compute the transport properties in terms of transmission and current–voltage characteristic. Our calculations show that the electron transport can open a conduction gap in the GNR/BNNR/GNR structure.