Flexible electrodes with supercapacitance were developed from highly mesoporous carbon fibers synthesized from lignin. Polyvinyl alcohol (PVA) facilitated the electrospinning of aqueous solutions of lignin and was used as a sacrificial polymer. Most importantly, PVA produced phase-separated domains for extreme surface area (>2000 m2 g-1) and mesoporous volume (0.7 cm3 g-1). An optimized sequential thermal treatment that initially included stabilization at 250 °C, allowed the formation of flexible, freestanding carbon networks upon PVA evolution to the gas phase and carbonization of the as-spun lignin-based fibers. Their main morphological and chemical characteristics were assessed by field emission scanning microscopy, transmission electron tomography reconstructions and Raman spectroscopy. The carbon fiber networks were used directly as electrodes with electrochemical double layer capacitance as determined by cyclic voltammetry and galvanostatic charge/discharge methods. Excellent electrochemical performance was demonstrated from the measured high rate capability and long-term cycling stability. The determined specific capacitance (∼205 F g-1 in 0.5 M Na2SO4 electrolyte) is one of the highest recorded for electrodes obtained from biopolymer precursors. Moreover, the electrical conductivity of the carbon fiber network (386 S m-1) was significantly higher, by two-orders of magnitude, than that obtained from the precursor (non-fibrous, powder) sample (2.47 S m-1). The remarkable performance of the synthesized electrodes is ascribed to the robust network morphology and mesoporosity obtained by soft-templating from the phase-separated sacrificial polymer. This is a demonstration of lignin valorization for novel application in advanced materials.