Using density functional theory calculations, we have studied the edge-functionalization of armchair graphene nanoribbons (AGNRs) with pentagonal-hexagonal edge structures. While the AGNRs with pentagonal-hexagonal edge structures (labeled (5,6)-AGNRs) are metallic, the edge-functionalized (5,6)-AGNRs with substitutional atoms opens a band gap. We find that the band structures of edge-functionalized (5,6)-N-AGNRs by substitution resemble those of defect-free (N-1)-AGNR at the Γ point, whereas those at the X point show the original ones of the defect-free N-AGNR. The overall electronic structures of edge-functionalized (5,6)-AGNRs depend on the number of electrons, supplied by substitutional atoms, at the edges of functionalized (5,6)-AGNRs.