Using a simple filtration method, we fabricate freestanding carbon-based composite paper electrodes (F-CCPEs), based on acid-treated carbon nanotubes (a-CNTs) and microporous carbon-based nanoplates containing numerous heteroatoms (H-CMNs). The F-CCPEs exhibited a high electrical conductivity of 2.3 × 102 S cm−1 and a high surface area of 1211.7 m2 g−1; moreover, they had numerous electroative heteroatoms and showed mechanical flexibility. Therefore, F-CCPEs without current collectors and binder show a superior electrochemical performance. In particular, the prepared F-CCPEs exhibit high capacitances of 275 and 148 F g−1 in aqueous and organic electrolytes, respectively. In addition, the specific energy density and specific power density of these F-CCPEs were found to be 63 Wh kg−1 and 140 kW kg−1, respectively, with good cyclic stability, even after 20,000 charge/discharge cycles.