Electrochemical proton storage plays an essential role in designing next-generation high-rate energy storage devices, e.g., aqueous batteries. Two-dimensional conjugated covalent organic frameworks (2D c-COFs) are promising electrode materials, but their competitive proton and metal-ion insertion mechanisms remain elusive, and proton storage in COFs is rarely explored. Here, we report a perinone-based poly(benzimidazobenzophenanthroline) (BBL)-ladder-type 2D c-COF for fast proton storage in both a mild aqueous Zn-ion electrolyte and strong acid. We unveil that the discharged C−O− groups exhibit largely reduced basicity due to the considerable π-delocalization in perinone, thus affording the 2D c-COF a unique affinity for protons with fast kinetics. As a consequence, the 2D c-COF electrode presents an outstanding rate capability of up to 200 A g−1 (over 2500 C), surpassing the state-of-the-art conjugated polymers, COFs, and metal–organic frameworks. Our work reports the first example of pure proton storage among COFs and highlights the great potential of BBL-ladder-type 2D conjugated polymers in future energy devices.