Fuel supply system, the regulation system for fuel delivery to fuel cell, is one of the most important auxiliary systems in a solid oxide fuel cell-gas turbine hybrid system. It plays a significant role in the dynamic performance and safety. Commonly, the fuel supply system is always simplified as a linear system which means that the relationship between valve opening and fuel flow rate is linear. However, the servo actuator and metering valve have some nonlinear characteristics such as hysteresis, dead zone, relay, and saturation. These nonlinear characteristics can directly affect the dynamic performance of the hybrid system. In this paper, a 328kW SOFC-GT hybrid system was taken as a research object. Firstly, a fuel supply system model considering the nonlinear characteristic was combined with the hybrid system. Then, the effect of dead zone-relay characteristic of servo amplifier was analyzed. The results show that the dead zone width has a great effect on the dynamic performance of the hybrid system. When the dead zone width is too small, the fuel flow rate will be oscillating causing unstable of the electrical characteristics in SOFC. The hybrid system will be stable with the increase of dead zone width. However, the larger dead zone width causes the hysteresis and the increase of the dynamic response time. At an improvement method with a two-dimensional fuzzy compensation was proposed. The results show that the fuzzy compensation can solve the oscillation problem caused by the dead zone-delay effectively. Finally, a servo actuator experiment system is developed based on an electro-hydraulic servo actuator facility and a software component of fuzzy compensator. The test rig was conducted an experiment to validate the simulation result. The results show that the experiment results match well with the simulation results.