A three-dimensional (3D) numerical model to predict the electrical properties of a nanocomposite made from an insulating polymer filled by carbon nanotubes (CNTs) is proposed. In this model, the percolation threshold is predicted by a statistical percolation model. Furthermore, a 3D resistor network model is proposed to predict the electrical conductivity of the nanocomposite. Experiments have been performed to verify the numerical results. For the application of the nanocomposite as strain sensors, by considering the tunnel effect, the resistor network model is extended to estimate the piezoelectricity. A strain sensor is made from this nanocomposite. Finally, both numerical and experimental results demonstrate that this new sensor possesses much higher sensitivity or gauge ratio compared with traditional strain gauges.