A metal–organic framework (MOF) having a redox active 1,4,5,8-naphthalenetetracarboxdiimide (NDI) derivative in its organic linker shows excellent rate performance as an electrode material for aqueous batteries thanks to its large pores. Among aqueous electrolytes examined, K⁺-based ones exhibit the highest rate performance, which is caused by the highest mobility of the smallest hydrated K⁺ ion not only in the aqueous electrolyte but also in the electrode. Since the use of a counter electrode with insufficiently small pores for the full-cell configuration offsets this merit, our study may lead to a conclusion that the maximum rate performance for aqueous batteries will be accomplished only through further elaboration of both electrode materials with sufficiently large pores, in which hydrated ions can travel equally fast as those in the electrolyte.