Proton conductivity through two-dimensional (2-D) hydrogen-bonding networks within a layered metal–organic framework (MOF) (NH4)2(H2adp)Zn2(ox)3·3H2O (H2adp = adipic acid; ox = oxalate) has been successfully controlled by cation substitution. We synthesized a cation-substituted MOF, K2(H2adp)Zn2(ox)3·3H2O, where the ammonium ions in a well-defined hydrogen-bonding network are substituted with non-hydrogen-bonding potassium ions, without any apparent change in the crystal structure. We successfully controlled the proton conductivity by cleavage of the hydrogen bonds in a proton-conducting pathway, showing that the 2-D hydrogen-bonding networks in the MOF truly contribute to the high proton conductivity. This is the first example of the control of proton conductivity by ion substitution in a well-defined hydrogen-bonding network within a MOF.