To solve the problem induced by serious nonlinear characteristic of the electro-hydrostatic actuator (EHA), and realize exact control of EHA, the mathematical model of EHA was derived, an exact linearization control law was obtained via nonlinear coordinate transformation and state feedback. The complicated nonlinear object was transformed into a simple linear system using the feedback linearization control strategy. Furthermore, the PID controller was combined with the feedback linearization strategy to fulfill an accurate position control. The simulation results show that the system has better rapidity and is free from overshoot, which demonstrate the correctness and feasibility of the control scheme.