This study investigates the electrical performance of a planar solid oxide fuel cell unit with cross-flow configuration when the fuel utilization gets higher and the fuel inlet flows are nonuniform. A numerical code, solving the two-dimensional, simultaneous, partial differential equations of mass, energy, and electrochemistry and neglecting the stack direction variation effect, is developed. The results show that the fuel utilization increases with a decrease in the molar flow rate, and the average current density decreases when the molar flow rate drops. In addition, nonuniform pattern A induces more severe happening of nonreaction area in the corner of the fuel exit and the air inlet. This nonreaction area deteriorates the average current density and then reduces the electrical performance to 7%. This study suggests that the fuel inlet manifold should be located far from the inlet of air, which is able to decrease the deterioration to below 3% when using nonuniform profile of pattern B. On the other hand, employing a suitable air flow rate, we can easily control the operating temperature of a solid oxide fuel cell unit and the effect of nonuniform inlet air flow rate on the temperature distribution becomes negligible.