To enhance the performance of anode-supported solid oxide fuel cell (SOFC), an electrochemical model has been developed in this study. The Butler-Volmer equation, Ohm’s law and dusty-gas model are incorporated to predict the activation, ohmic and concentration overpotentials, respectively. The optimal cell microstructure and operating parameters for the best current-voltage (J-V) characteristics have been sought from the information of the exchange current density and gas diffusion coefficients. As the cell temperature rises, the activation and ohmic overpotentials decrease, whereas the concentration overpotential increases due to the considerable reduction of gas density at the elevated temperature despite the increased diffusion coefficient. Also, increasing the hydrogen molar fraction and operating pressure can further augment the maximum cell output. Since there exists an optimum electrode pore size and porosity for maximum cell power density, the graded electrode has newly been designed to effectively reduce both the activation and concentration overpotentials. The results exhibit 70% improved cell performance than the case with a non-graded electrode. This electrochemical model will be useful to simply understand overpotential features and devise the strategy for optimal cell design in SOFC systems.