We study analytically, based on the tight-binding model, the electronic band structure of armchair AA-stacked bilayer graphene nanoribbons (BLGNRs) in several regimes. We apply hard-wall boundary conditions to determine the discretion dominating on the Bloch wavefunctions in the confined direction. First we consider an ideal case, perfect nanoribbons without any edge deformation, and show that their electronic properties are strongly size-dependent. We find that the narrow armchair AA-stacked BLGNRs (similar to single-layer graphene nanoribbons) may be metallic or semiconducting depending on their width determined by the number of dimer lines across the ribbon width, while the wide ribbons are metallic. Then we show that, when the edge deformation effects are taken into account, all narrow armchair AA-stacked BLGNRs become semiconducting while the wide ribbons remain metallic. We also investigate effects of an electric filed applied perpendicular to the nanoribbon layers and show it can be used to tune the electronic properties of these nanoribbons leading to a semiconducting-to-metallic phase transition at a critical value of the electric field which depends on the nanoribbon width. Furthermore, in all regimes, we calculate the corresponding wavefunctions which can be used to investigate and predict various properties in these nanoribbons.