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Electronic structures of graphene nanoribbons with armchair edges (AGNRs) containing N-substitutional impurity have been investigated, using ab initio density functional theory. It is shown that the electronic structures of the doped AGNRs are different from those of doped carbon nanotubes (CNTs). N introduces an impurity level above the conduction band minimum (CBM) in the AGNRs while an impurity level introduced by N is below the CBM in the CNTs. This character can be explained as a consequence of the edge polarization effects, which ionize the impurity level so that the relevant charge carriers occupy the conduction bands, which is independent of curvature and doping site. Although the N-doped AGNR and CNT are all n-type semiconductors, an implication of the result is that edge polarization effects could make some properties of the N-doped AGNRs different from those of N-doped CNTs. It suggests the possibility to make 1-D doped structures with novel physical and device characteristics.