Stable cathodes with multiple redox-active centres affording a high energy density, fast redox kinetics and a long life are continuous pursuits for aqueous zinc-organic batteries. Here, we achieve a high-performance zinc-organic battery by tuning the electron delocalization within a designed fully conjugated two-dimensional hydrogen-bonded organic framework as a cathode material. Notably, the intermolecular hydrogen bonds endow this framework with a transverse two-dimensional extended stacking network and structural stability, whereas the multiple C = O and C = N electroactive centres cooperatively trigger multielectron redox chemistry with super delocalization, thereby sharply boosting the redox potential, intrinsic electronic conductivity and redox kinetics. Further mechanistic investigations reveal that the fully conjugated molecular configuration enables reversible Zn2+/H+ synergistic storage accompanied by 10-electron transfer. Benefitting from the above synergistic effects, the elaborately tailored organic cathode delivers a reversible capacity of 498.6 mAh g−1 at 0.2 A g−1, good cyclability and a high energy density (355 Wh kg−1).