Using the Green’s function method, we investigate the effect of vacancies on conductance and local density of states (LDOS) in zigzag graphene nanoribbons within a symmetric and asymmetric potential wells. The results differ from ideal ribbons in that there are no conductance plateaus and a decline in conductance for varied N (number of atoms in the unit cell) and M (number of unit cells) values following vacancy incorporation. LDOS and conductance in symmetrical and asymmetrical circumstances are examined alongside vacancies and accordingly, they are affecting the respective edge states.