Graphene has great potential for ultra-sensitive strain sensors applications due to its high mechanical strength and good compatibility with the traditional semiconductor process. In the current study, we investigated the effect of tensile and bending deformations on the electronic states of graphene nanoribbons (GNRs) using density functional theory (DFT) to clarify the underlying mechanism of the piezoresistive properties of graphene. It is found that the electronic structure of armchair graphene nanoribbons (AGNRs) is very sensitive to the tensile deformation. When a uniaxial tensile stress is applied to AGNRs with width Na = 10, the band structure is modified, leading to the change in band gap approximately from 0 eV to 1.0 eV. The band gap values of bent AGNRs decrease significantly when the maximum local dihedral angle exceeds a critical value due to the orbital hybridization. Based on these knowledge, we fabricated a strain sensor using the graphene film grown by thermal chemical vapor deposition (CVD) method on Cu foil. The strain sensor is fabricated directly on the graphene-coated Cu foils by using the standard photolithography process and reactive ion etching (RIE) and then transferred onto a stretchable and flexible polydimethysiloxane (PDMS) substrate. The one-dimensional tensile test and three-dimensional bending test are performed to investigate the piezoresistive properties. A gauge factor 3.4 was achieved under the tensile deformation. The fabricated strain sensor also exhibits good performance to detect bending deformation.