Oxide ion and proton conductors, which exhibit high conductivity at intermediate temperature, are necessary to improve the performance of ceramic fuel cells. The crystal structure plays a pivotal role in defining the ionic conduction properties, and the discovery of new materials is a challenging research focus. Here, we show that the undoped hexagonal perovskite Ba₇Nb₄MoO₂₀ supports pure ionic conduction with high proton and oxide ion conductivity at 510 °C (the bulk conductivity is 4.0 mS cm⁻¹), and hence is an exceptional candidate for application as a dual-ion solid electrolyte in a ceramic fuel cell that will combine the advantages of both oxide ion and proton-conducting electrolytes. Ba₇Nb₄MoO₂₀ also showcases excellent chemical and electrical stability. Hexagonal perovskites form an important new family of materials for obtaining novel ionic conductors with potential applications in a range of energy-related technologies.