For a solid oxide fuel cell, temperature gradient has a great effect on its efficiency and durability. In recent years, several observers are developed to estimate the temperature gradient. However, the temperature gradient control strategies with suitable observers are not seen. Therefore, a compound nonlinear controller based on a high-order sliding mode observer is proposed to control the temperature gradient at desired values to improve the solid oxide fuel cell performance. The high-order sliding mode observer is firstly employed to estimate immeasurable internal temperature. Under the interference of the variations in the initial values of the internal states and measurement noises, the high-order sliding mode observer can estimate the internal temperature distribution with a high precise and a fast convergence. The compound controller which includes a feedback linearization controller and a feedforward controller is then applied to regulate the estimated temperature gradient. During load current changes, the compound controller has the best dynamic performance compared with the feedback linearization controller. However, the observed temperature gradient with the two control strategies can both reach the desired value.