In this study, a numerical model is built to analyze the leakage current of a proton conductor solid oxide fuel cell. The transports of electron-hole and proton transfer in a mixed conductor electrolyte is described by the Nernst-Planck equation. The model is validated using experimental data. The leakage current, potential distribution, Faraday efficiency and energy efficiency are analyzed. When the output voltage of the fuel cell is greater than 0.5 V, the leakage current will cause the energy efficiency in a significant reduction. The lower the temperature, the lower the leakage current density. Lowering the temperature will improve the Faraday efficiency and energy efficiency of the fuel cell. Lower output voltage helps improve the Faraday efficiency.