Supercapacitors can deliver high electrical power because of fast ion adsorption/desorption on the surface or surface redox reactions, which, in turn, restrict their energy density. To break surface-storage ceiling and further improve the energy density, here, we develop a cost-effective, layered material made of amorphous metal-organic nanosheets, Ni-p-phenylenediamine (Ni-pPD), with a large intersheet spacing of 1.6 nm for its robust and highly reversible intercalation reaction with tetraethylammonium cations. When coupled with activated carbon cathode, the 230 μm-thick Ni-pPD anode shows a high gravimetric capacitance (259 F g−1) and a high areal capacitance (2.9 F cm−2) at 2 A g−1 within a wide potential window of 2.85 V in the organic electrolyte of tetraethylammonium tetrafluoroborate/acetonitrile. In-situ electrochemical atomic force microscopy reveals that high kinetics at high potentials are attributed to the increased intersheet spacing under large polarization, demonstrating structural advantages of this novel material and its great potential for real-world applications.