A mathematical model for proton-conductive solid oxide fuel cell (H-SOFC) is presented in this work. The analysis and optimization of fuel cell components is to help the design and fabrication of H-SOFCs which are experimentally studied by the current authors. The mathematical model considers mass transfer and concentration polarization using an average mass transfer model analogous to the convective heat transfer in a duct flow and across a wall. The average concentrations of species at interfaces of electrodes/electrolyte at any operating current densities are calculated, and therefore the species concentrations are included in the calculation for activation polarizations. The ohmic loss is considered through analysis of a circuit simulating the electron and proton conduction. Empirical coefficients for the exchange current density in activation polarization analysis were determined and validated by referring to experimental results from multiple publications. Parametric analysis has also been done to show how the performance of H-SOFC is dependent on properties of fuel cell components.