Polyaniline (PANI) has been regarded as a promising electrode material for energy storage devices. However, unsatisfactory cycling stability seriously restricts its practical application. Herein, the nitrogen-doped porous graphene (NPG) film-supported vertically aligned polyaniline nanocones (NPG@PANI) flexible cathodes were synthesized by electrochemical polymerization. The as-prepared NPG@PANI displays unique porous morphology and strong π-π stacking interaction, which facilitates charge transportation and suppresses the dissolution as well as relieves volume changes of PANI during charging-discharging process. Moreover, a novel quasi-solid-state polymer electrolyte (QPE) of porous acrylate rubber/tetraethylammonium tetrafluoroborate-acetonitrile (pACM/Et4NBF4-AN) with enhanced ionic conductivity was prepared to match with π-conjugated polymer electrodes, which helps to restrain the dissolution and the structure degradation of electrodes. To enhance the energy density, the organic asymmetric flexible supercapacitor (oAFSC) was assembled by NPG@PANI cathode, NPG supported-poly(1,5-diaminoanthraquinone) (NPG@PDAA) anode and pACM/Et4NBF4-AN QPE. The as-assembled oAFSC shows high energy density (6.18 mWh cm−3), good rate capability and superior cycling stability (88.7% capacitance retention after 10000 cycles).