Solid oxide fuel cell (SOFC) that is operated at high temperature (650∼1000 °C), have many advantages such as high efficiency, useful waste heat and fuel flexibility. However, due to its high temperature operation, it is hard to obtain optimal cell design and parameters for improving SOFC performances through experimental works. Mathematical models have been developed to understand and elucidate effects of various designs and operation parameters on SOFC performances, as well as accelerate SOFC developments. In this work, various electrochemical phenomena of SOFC have been investigated using the change of operating parameters (e.g, temperature, pressure, gas composition, pore size and porosity). The typical operating conditions for P H2O, P H2 and P O2 were 0.03, 0.97 and 0.21 bar. Butler-Volmer equation, dusty-gas model and Ohm's law were incorporated to determine the activation, concentration, ohmic overpotential. To verify good agreement with experimental data the exchange current density and gas diffusion coefficient have been sought, depending on operational conditions (temperature, pressure and gas composition) and the cell microstructures (porosity and pore size). As the cell temperature increases, 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. As the triple phase boundary (TPB) length which is closely related with the pore size, grain size, and overlap of particles principally affects the activation overpotential, activation overpotential can be minimized at maximum TPB length by controlling the pore size and porosity. Furthermore, it is noted that the concentration overpotential decreases with increasing pore size and porosity due to the increased Knudsen diffusion. There were optimal values of electrode pore size and porosity for better cell performance. From the fact that there exists an optimum of 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 graded electrode can offer both sufficient reactive area and good gas transport. In typical non-graded electrode case, decreasing pore size and porosity for reducing activation overpotential makes the concentration overpotential greatly larger. Such opposing effect can be eliminated by a well-defined graded electrode. Comparing with non-graded electrode, a micro-structural graded electrode can be classified into two different types, namely porosity grading and pore size grading, respectively. It is assumed that both porosity and pore size increase linearly from the electrode/electrolyte interface to the electrode surface. The results exhibit 70% improved cell performance than 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. The simulation data quantitatively agreed with experimental data of anode-supported tubular SOFC.