Herein, we developed a highly conductive and lightweight membrane substrate based on the ethylene–vinyl acetate copolymer (EVA), carbon nanotubes (CNTs) and lens wiping paper, and demonstrated its implementation as high-performance mechanical support for MnO2 in supercapacitors. The 45 s-MnO2/EVA/40 wt%CNT electrode exhibited a high capacitance (0.126 F cm−2 at 0.5 mA cm−2) with excellent flexibility. Furthermore, the fabricated devices based on these 45 s-MnO2/EVA/40 wt%CNT electrodes exhibited excellent flexibility and stability (85% of its initial capacitance retained after 800 bending cycles) and achieved a high energy density of 9.4 Wh kg−1 at 6780 W kg−1.