In this work, we prepared network-structured carbon nanofibers using polyacrylonitrile blends (PAN150 and PAN85) with different molecular weights (150,000 and 85,000 g mol−1) as precursors through electrospinning/hot-pressing methods and stabilization/carbonization processes. The obtained PAN150/PAN85 polymer nanofibers (PNFs; PNF-73, PNF-64 and PNF-55) with different weight ratios of 70/30, 60/40 and 50/50 (w/w) provided good mechanical and electrochemical properties due to the formation of physically bonded network structures between the blended PAN nanofibers during the hot-processing/stabilization processes. The resulting carbonized PNFs (cPNFs; cPNF-73, cPNF-64, and cPNF-55) were utilized as anode materials for supercapacitor applications. cPNF-73 exhibited a good specific capacitance of 689 F g−1 at 1 A g−1 in a three-electrode set-up compared to cPNF-64 (588 F g−1 at 1 A g−1) and cPNF-55 (343 F g−1 at 1 A g−1). In addition, an asymmetric hybrid cPNF-73//NiCo2O4 supercapacitor device also showed a good specific capacitance of 428 F g−1 at 1 A g−1 compared to cPNF-64 (400 F g−1 at 1 A g−1) and cPNF-55 (315 F g−1 at 1 A g−1). The cPNF-73-based device showed a good energy density of 1.74 W h kg−1 (0.38 W kg−1) as well as an excellent cyclic stability (83%) even after 2000 continuous charge–discharge cycles at a current density of 2 A g−1.