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Based on the tight-binding approximation, analytical solutions of the energy dispersion and band gap of armchair-edge graphene nanoribbons (AGNRs) under uniaxial strains are derived. Subsequent numerical results on band gap are found to be consistent with the analytical solutions. It is shown that the energy gap of AGNRs is sensitive to the uniaxial strains and is predicted to change with a V shape as a function of the applied uniaxial strain. It is interesting to find that the uniaxial strain could induce metal-semiconductor transition for the AGNRs with a width of n=3m+2 ((3m + 2)-AGNRs) and semiconductor-metal-semiconductor phase transition for the (3m + 1)-AGNRs, but no phase transition is induced for the 3m-AGNRs.