Using multifunctional organic ligands with multiple acidic groups (carboxylate and sulfonate groups) to synthesize metal-organic frameworks (MOFs) bearing effective H-bond networks is a promising strategy to obtain highly proton conductive materials. In this work, a highly stable two-dimensional MOF, [CuII5CuI2(μ3-OH)4(H2O)6(L)2(H2L)2]·3H2O (denoted as YCu161; H3L = 6-sulfonaphthalene-1,4-dicarboxylic acid) containing mixed-valence [CuII5CuI2(μ3-OH)4]8+ subunits, was successfully prepared. It exhibited excellent stability and temperature- and humidity-dependent proton conduction properties. Its optimal proton conductivity reached 1.84 × 10-3 S cm-1 at 90 °C and 98% relative humidity. On the basis of a crystal structure analysis, water vapor adsorption test results, and activation energy calculations, we deduced the proton conduction pathway and mechanism. Apparently, uncoordinated sulfonic and carboxyl groups and a network of abundant H-bonds inside the framework were responsible for the efficient proton transfer. Therefore, the strategy of selecting suitable bifunctional ligands to construct two-dimensional Cu-cluster-based MOFs with excellent proton conductivity is feasible.