We investigate the impact of interlayer mismatch on the electronic properties of bilayer graphene nanoribbons (BGNRs) with armchair-edges in terms of the total energy and electronic structures by first principle calculations. Simulation results show that in-plane misalignments require little energy and a large variation in the energy bandgap (EG) can be observed. Based on the resulting atomic configurations due to the misalignments, the details of the observed relationship between bandgap and the lattice mismatch are investigated. It is observed that in general, misalignment in the transverse direction results in a decrease in the interaction between the two layers, giving rise to a larger EG. On the other hand, misalignment in the longitudinal direction, i.e. along the edges, leads to an oscillation in EG due to the periodic change of the GNR stacking order. A combination of these movements results in a complex variation of EG, which introduces great uncertainty in electronic devices. However, such a phenomenon could also be used in various kinds of nanoelectromechanical systems as it provides a large change in electronic properties with a small movement.