In order to remedy the deficiency of existing flexible strain sensors in health monitoring, an elastic composite material with piezoresistive effect was prepared by the solution blending and solvent evaporation method, with reduced graphene oxide (rGO) as conductive filler, cellulose nanofiber (CNF) as dispersant and structural skeleton, and polydimethylsiloxane (PDMS) as elastic matrix. The microstructure, mechanical properties, electrical conductivity and electromechanical performance of the composite were investigated. Results show that CNF can significantly improve the dispersion of rGO in the PDMS matrix, and help to form stable three-dimensional reinforcing and conductive networks, increasing the elastic modulus and conductivity of the composite. When the mass fractions of rGO and CNF in PDMS were 10% and 3%, respectively, the elastic modulus of the composite reached the maximum value of 2.53 MPa, with the electrical conductivity of 0.34 S/m. When the strain of the composite film was less than 10%, the relative variation of resistance was linear with the strain. The maximum sensitivity coefficient was 63, and the corresponding mass fractions of rGO and CNF were 10% and 3%, respectively. When the strain was more than 10%, the resistance varied exponentially. The electromechanical response mechanism of the composite was analyzed, and the composite was applied to the monitoring of fatigue cracks of materials or components. A film sensor of stress intensity factors was designed, and its feasibility was verified by theoretical analysis.