Stretchable conductive polymers have aroused extensive interest in research recently due to their hi-tech applications in the fields of novel electronics, particularly for flexible electronic displays, smart textiles, medical electronics, sensors and actuators. In this study, we describe a novel elastic conductive nanocomposite made with multiwall carbon nanotubes (MWNTs) and polyurethane (PU). With the aid of an ionic liquid and under the condition of uniaxial tension, the MWNTs can form well-developed conducting networks in the PU matrix. The developed nanocomposite inherited advantageous properties from its constituents, namely the high conductivity from MWNTs, and the high elastomeric mechanical properties from the PU. Moreover, the stretchable conductive nanocomposite can be uniaxially stretched up to 100% without significant variation in electrical conductivity. The measurement of temperature dependent conductivity indicates that a 3D hopping mechanism dominates the conductivity of MWNTs.