A proton-conductive solid oxide fuel cell (H-SOFC) has the advantage of operating at higher temperatures than a PEM fuel cell, but at lower temperatures than a SOFC. This study proposes a mathematical model for an H-SOFC in order to simulate the performance and optimize the flow channel designs. The model analyzes the average mass transfer and species' concentrations in flow channels, which allows the determination of an average concentration polarization in anode and cathode gas channels, the proton conductivity of electrolyte membranes, as well as the activation polarization. An electrical circuit for the current and proton conduction is applied to analyze the ohmic losses from an anode current collector to a cathode current collector. The model uses relatively less amount of computational time to find the V-I curve of the fuel cell, and thus it can be applied to compute a large amount of cases with different flow channel dimensions and operating parameters for optimization. The modeling simulation results agreed satisfactorily with the experimental results from literature. Simulation results showed that a relatively small total width of flow channel and rib, together with a small ratio of the rib's width versus the total width, are preferable for obtaining high power densities and thus high efficiency.Keywords: proton-conductive SOFC; mathematical model; optimization of gas channels