In dual-redundancy electro-hydrostatic actuators (EHAs), the dual pumps are mainly designed for safety, where the cylinder is controlled mainly by one pump while the other one is standby for redundancy. However, such a strategy is basically like a single-pump-controlled system, and the flow from the pump may be inaccurate when the cylinder moves slowly, which will affect the motion control performance. A new dual-redundancy EHA is designed, and a series of corresponding operation modes are developed, enabling differential operation of the dual pumps. With the proposed operation modes, the inevitable flow inaccuracy problem of the single pump can be addressed through the coordination control of the dual pumps. In order to achieve better motion tracking performance, a model-based backstepping controller is synthesized, where the nonlinearities and uncertainties of the EHA are handled by model compensation and robust feedback design. Comparative simulations with existing control methods for EHAs are conducted and better motion tracking precision is achieved, especially during low-speed motion.