Nanocomposites based on a thermoplastic elastomer, poly[styrene-b-(ethylene-co-butylene)-b-styrene] triblock copolymer (SEBS), and multiwalled carbon nanotubes (MWCNTs) were fabricated using a high-shear processing technique. The MWCNTs were homogeneously dispersed in the SEBS matrix, even at an MWCNT concentration of 15 wt %. The addition of MWCNTs to the elastomer significantly enhanced its electrical conductivity and mechanical properties, including increased modulus and tensile strength, with only a slight loss of stretchability. The fabricated nanocomposites loaded with 15 wt % MWCNT showed an excellent stretchability of more than 600% and a high strain recovery under mechanical deformation. Moreover, the conductivity of fabricated conductive nanocomposites only slowly decreases with uniaxial stretching. Therefore, a stretchable and elastic conductive polymer nanocomposite was Successfully fabricated. In addition, the effect of the uniformly dispersed MWCNTs on the SEBS microphase separation behaviors was also investigated by small-angle X-ray scattering (SAXS), synchrotron SAXS, and transmission electron microscopy (TEM). The results indicate that the homogeneously dispersed MWCNTs not only disturb the microphase-separated structure of SEBS but also decrease its order-disorder transition temperature.