The design of Faradaic battery electrodes that exhibit high rate capability and long cycle life equivalent to those of the electrodes of electrical double-layer capacitors is a big challenge. Here we report a strategy to fill this performance gap using the concept of Grotthuss proton conduction, in which proton transfer takes place by means of concerted cleavage and formation of O–H bonds in a hydrogen-bonding network. We show that in a hydrated Prussian blue analogue (Turnbull’s blue) the abundant lattice water molecules with a contiguous hydrogen-bonding network facilitate Grotthuss proton conduction during redox reactions. When using it as a battery electrode, we find high-rate behaviours at 4,000 C (380 A g−1, 508 mA cm−2), and a long cycling life of 0.73 million cycles. These results for diffusion-free Grotthuss topochemistry of protons, in contrast to orthodox battery electrochemistry, which requires ion diffusion inside electrodes, indicate a potential direction to revolutionize electrochemical energy storage for high-power applications.