When cracks appear in reinforced concrete (RC) structures, the tensile load will be borne by steel bars with high ductility, resulting in a large deformation. Traditional strain sensors have difficulties in achieving good performance for large deformations in concrete structures. In this paper, based on a laser-induced graphene (LIG) technique, a flexible sensor is proposed for monitoring large deformations of concrete structures. Polyimide film is used as the carbon precursor to prepare LIG through laser scanning and then LIG is transferred onto a polydimethylsiloxane (PDMS) substrate to form the flexible sensor. The calibration and performance verification of the flexible sensor are completed through tensile tests. The applicability of the flexible sensor in monitoring large deformations of concrete is verified through beam bending experiments. The fatigue resistance of the flexible sensor is verified through fatigue tests on a full-scale beam. The experimental results showed that the flexible sensor has the advantages of low cost, simple preparation, and stable performance, making it suitable for applications in the field of large deformation monitoring of RC structures.