A study was conducted to present evidence for the Peierls effect in a strained armchair graphene nanoribbons (AGNR) with H-saturated edges and 11 dimer lines, treated with density functional theory (DFT) within the generalized gradient approximation. The strained AGNR was considered optimized when the convergence criteria of 1 × 10-5 in the gradient, 1 × 10-4 in the displacement and 1 × 10-7 a.u. in energy were met. Calculations were considered explicitly only atoms located in one primitive motif under periodic boundary conditions. A set of 123 K points uniformly spaced along the one-dimensional Brillouin zone was used to achieve good convergence in reciprocal space integration. Investigations revealed that the uncovered electron-phonon interaction effect was the mechanism that prevented the onset of the metallic state under ε obtained in other DFT calculations employing several approximate functionals.