Graphene has exhibited great potential for the application of next-generation electronic devices. However, undesirable interface stress induced during graphene transfer and device fabrication process causes the deformation of graphene, resulting in the change in its electronic properties. In this study, the effect of three-dimensional mechanical loading such as tensile, bending and folding deformations on the electronic states of armchair graphene nano-ribbons (AGNRs) is investigated based on density functional theory (DFT) calculation. It was found that the electronic structure of AGNRs shows differential sensitivity to various deformation modes. The effect of uniaxial tension on the electronic conductivity of AGNRs was also analyzed using quantum transport simulation and it was found that the uniaxial tensile strain changes the band gap of AGNRs, resulting in the change in the electronic conductivity. The current-strain (I-ε) relationship of AGNRs strongly depends on the length of the strained area. This understanding paves the way for the development of highly sensitive GNRs strain sensors.