Extremely elastic and sensitive strain gauge sensors are highly demanded to keep track of strains in flexible electronics, skin deformation, and human movement. This report discusses a new approach to fabricate a stretchable, electrically conductive and sensitive strain gauge sensor which uses a polymeric nanofibrous composite of thermoplastic polyurethane (TPU) elastomer and conductive poly (3,4-ethylene dioxythiophene) poly(styrene sulfonate) (PEDOT: PSS) polymer as its basis. The nanofibrous composite was prepared using wet electrospinning technique. The designed TPU/PEDOT: PSS membrane loaded on a silicon rubber (SR) substrate holds an electrical resistance of 3 KΩ and a stable gauge factor of 20 up to 40% strains at room temperature. A single Wheatstone bridge was implemented to calibrate a micro-patterned strain sensor grid for voltage output versus an applied bending moment/force. The obtained results inferred that the fabricated sensor could be used to sense rapid and minute deformation actions in a wide range of engineering applications.