BaCe0.7Zr0.2Nd0.1O3−α ceramic was prepared by solid state reaction. Phase composition, surface and fracture morphologies of the material were characterized by using XRD and SEM, respectively. Chemical stability against carbon dioxide and water steam at the high temperature was tested. The conductivity and ionic transport number of the material were measured by ac impedance spectroscopy and gas concentration cell methods in the temperature range of 500–900°C in wet hydrogen and wet air, respectively. Using the ceramic as solid electrolyte and porous platinum as electrodes, the hydrogen‐air fuel cell was constructed, and the cell performance at the temperature from 500 to 900°C was examined. The results indicate that BaCe0.7Zr0.2Nd0.1O3−α was a single phase perovskite‐type orthorhombic system, with high density and good chemical stability in carbon dioxide and water steam atmospheres at the high temperature. The conductivity of the material in wet hydrogen and wet air was increased as the temperature rises. In wet hydrogen, the material was a pure protonic conductor with the protonic transport number of 1 from 500 to 600°C, a mixed conductor of proton and electron with the protonic transport number of 0.973–0.955 from 700 to 900°C. In wet air, the material was a mixed conductor of proton, oxide ion and electron hole. The protonic transport numbers were 0.002–0.003, and the oxide ionic transport numbers were 0.124–0.179. The fuel cell could work stably. At 900°C, the maximum short‐circuit current density and power output density were 156 mA·cm−2 and 40 mW·cm−2, respectively.