The effect of tensile uniaxial strain on the non-parabolic electronic band structure of armchair graphene nanoribbon(AGNR) is investigated.In addition,the density of states and the carrier statistic based on the tight-binding Hamiltonian are modeled analytically.It is found that the property of AGNR in the non-parabolic band region is varied by the strain.The tunable energy band gap in AGNR upon strain at the minimum energy is described for each of n-AGNR families in the non-parabolic approximation.The behavior of AGNR in the presence of strain is attributed to the breakable AGNR electronic band structure,which varies the physical properties from its normality.The linear relation between the energy gap and the electrical properties is featured to further explain the characteristic of the deformed AGNR upon strain. The effect of tensile uniaxial strain on the non-parabolic electronic band structure of armchair graphene nanoribbon (AGNR) is investigated. In addition, the density of states and the carrier statistic based on the tight-binding Hamiltonian are modeled analytically. It is found that the property of AGNR in the non-parabolic band region is changed by the strain. The tunable energy band gap in AGNR upon strain at the minimum energy is described for each of n-AGNR families in the non-parabolic approximation. The behavior of AGNR in the presence of strain is attributed to the breakable AGNR electronic band structure, which varies the physical properties from its normality. the linear relation between the energy gap and the electrical properties is featured to further explain the characteristic of the deformed AGNR upon strain.