A comprehensive 3D computational fluid dynamics (CFD) model is developed for a bi-electrode supported cell (BSC) solid oxide fuel cell (SOFC). The model includes complicated transport phenomena of mass/heat transfer, charge (electron and ion) migration, and electrochemical reactions. The uniqueness of the modeling study is that functionally graded porous electrode property is taken into account, including not only linear but also nonlinear porosity distributions. The model is validated using experimental data from open literature. Numerical results indicate that BSC performance is strongly dependent on both operating conditions and porous microstructure distributions of electrodes. Using the proposed fuel/gas feeding design, the uniform hydrogen distribution within the porous anode is achieved; the oxygen distribution within the cathode is dependent on porous microstructure distributions as well as pressure loss conditions. Simulation results also show that fairly uniform temperature distribution can be obtained with the proposed fuel/gas feeding design. This modeling work can provide a pre-experimental analysis and guide experimental designs for BSC test.