New proton conducting materials are needed to enable operation of proton exchange membrane fuel cells at intermediate temperatures and conditions of low humidity. We report that graphane functionalized with amine groups (graphamine) can conduct protons in the complete absence of water, as demonstrated by ab initio density functional theory molecular dynamics simulation. Graphamine’s intrinsic proton conductivity is due to its contiguous network of hydrogen bonds, which facilitate a “Grotthuss-like” proton hopping mechanism. Our calculations show that graphamine is an electronic insulator having a direct band gap of 3.08 eV. Our calculated phonon density of states and elastic properties indicate that graphamine is mechanically stable, with an in-plane Young’s modulus of 262 J/m2, which lies in between the values for graphene and graphane. We predict that graphamine has the transport, electronic, and structural properties required for a viable anhydrous proton conduction membrane material.