The electro-hydrostatic actuator (EHA) is a kind of power-by-wire (PBW) actuator that converts the electrical power into localized hydraulic power for flight control. In order to solve the problem of flow mismatching in the asymmetric cylinder, this paper presents a novel EHA which applies a three-ports fixed displacement pump to work with the asymmetric cylinder. The working principle of the novel EHA is introduced, and its nonlinear mathematical model is built. The sliding-mode control is proposed to control the position loop of the EHA. The controller structure of EHA is built including the position control using sliding-mode control, the speed control using PI, and the current control using PI. The model of mechanical parts including the permanent magnet synchronous motor (PMSM), controller and hydraulic parts are built in the SIMULINK. Simulation results show that the sliding-mode control improves the dynamic response and control accuracy compared with the traditional classic PID.