A general method is described to prepare high-performance conductive polymer fibers or tapes. In this method, bicomponent tapes/fibers containing two layers of conductive polymer composites (CPCs) filled with multiwall carbon nanotubes (MWNT) or carbon black (CB) based on a lower-melting-temperature polymer and an unfilled polymer core with higher melting temperature are fabricated by a melt-based process. Morphological control of the conductive network formed by nanofillers is realized by solid-state drawing and annealing. Information on the morphological and electrical change of the highly oriented conductive nanofiller network in CPC bicomponent tapes during relaxation, melting, and crystallization of the polymer matrix is reported for the first time. The conductivity of these polypropylene tapes can be as high as 275 S m−1 with tensile strengths of around 500 MPa. To the best of the authors' knowledge, it is the most conductive, high-strength polymer fiber produced by melt-processing reported in literature, despite the fact that only ∼5 wt.% of MWNTs are used in the outer layers of the tape and the overall MWNT content in the bicomponent tape can be much lower (typically ∼0.5 wt.%). Their applications could include sensing, smart textiles, electrodes for flexible solar cells, and electromagnetic interference (EMI) shielding. Furthermore, a modeling approach was used to study the relaxation process of highly oriented conductive networks formed by carbon nanofillers.