The analytic relationship among armchair graphene nanoribbons' bond angles and bond lengths and the uniaxial tensile strain along armchair edge was established by the static method. By the tight binding method, the relationship among armchair graphene nanoribbons's energy band and band gap and strain was calculated. The results show that the application of a small uniaxial strain leads to variation of energy subband spacing, which opens a band gap for metallic AGNRs and modifies the band gaps for semiconducting AGNRs near the Fermi level. Energy gap displays linear periodic variation with the ...