It is difficult to produce rubbery polymer nanofibers, that is, polybutadiene, by the method of electrospinning, since during electrospinning rubbery polymer fibers join and entangles due to their low T-g. For this reason, it is not easy to achieve the fiber form out of these polymers. Homogeneously electrospun carbon nanotubes (CNT)-filled polybutadiene (PBu) and poly(ethylene oxide) (PEO) composite elastomeric fibers exhibit distinctive physical features such as uniform fiber diameter and distribution with significant improvements in thermomechanical properties. Controlled hydrophilicity/hydrophobicity with the components allows to generate homogenous, thermally stable and stretchable bio-composite scaffold, and fibrous antibacterial membrane scaffolds out of PBu/PEO/CNT composite. We have combined the exciting properties of PEO with high pore density with the rubber elasticity of PBu via dissolving them in a dichloromethane/ethyl acetate organic solvent, and subsequently producing electrospun woven fibers with different PBu/PEO ratios. Frequency-dependent thermomechanical characterization via dynamic mechanical analysis reveals pronounced changes in the onset and extent of melting, as well as the storage and loss modulus values at the onset of melting, in particular when small amounts (1.25% by wt%) of CNTs are present. The characteristic bands were detected for the PBu/PEO and PBu/PEO/CNT samples by means of Raman and Fourier-transform infrared spectroscopy. CNT addition increases the hydrophobicity via the increase in roughness as attained by atomic force microscopy.