In this work, the piezoresistive behavior of a strain sensor made from a polymer/carbon nanotube nanocomposite has been investigated. To underpin the working principle of the sensor, we propose an improved 3D statistical resistor network model by incorporating the tunneling effect among randomly distributed carbon nanotubes (CNTs) in a polymer matrix.Moreover, the strain sensor has been experimentally fabricated from a polymer nanocomposite with multi-walled carbon nanotube (MWNT) fillers. The piezoresistivity of this nanocomposite strain sensor has been experimentally investigated. The numerical results obtained from the 3D statistical resistor network model combined with the fiber reorientation model agree very well with the experimental measurements. From numerical and experimental results, as compared to the traditional strain gauges, much higher sensitivity can be obtained in this nanocomposite sensor. The tunneling effect is highlighted to be the major working mechanism of the sensor under small strains. By using the proposed successful numerical model, the influences of various parameters on the sensitivity of the new sensor have been numerically investigated in detail. The influence of various experimental parameters on the sensitivity of the sensor has also been studied. Both results have shown that higher resistance of the sensor leads to higher sensitivity of the sensor. Furthermore, the different behaviors of the sensor under tension and compression have been investigated.