With fast (de)coordination kinetics, the smallest and the lightest proton stands out as the most ideal charge carrier for aqueous Zn-organic batteries (ZOBs). Hydrogen-bonding networks with rapid Grotthuss proton conduction is particularly suitable for organic cathodes, yet not reported. We report the supramolecular self-assembly of cyanuric acid and 1,3,5-triazine-2,4,6-triamine into organic superstructures through in-plane H-bonds and out-of-plane π-π interaction. The supramolecular superstructures exhibit highly stable lock-and-key H-bonding networks with an ultralow activation energy for protonation (0.09 eV vs. 0.25 eV of zincification). Then, high-kinetics H+ coordination is prior to Zn2+ into protophilic C=O sites via a two-step nine-electron reaction. The assembled ZOBs show high-rate capability (135 mAh g-1 at 150 A g-1), high energy density (267 Wh kg-1cathode) and ultra-long life (50,000 cycles at 10 A g-1), becoming the state-of-the-art ZOBs in comprehensive performances.