Characterized by high power-to-weight ratio, modularity and energy efficiency, electro-hydrostatic actuators (EHAs) have been successfully applied to aircrafts and submarines, where high precision and repeatability are in high demand. The position tracking performance, however, can be inevitably affected by parametric uncertainties and uncertain nonlinearities. Model inaccuracy or system variations normally require a large loop gain to achieve robust performance, which leads to over-design. Leakage in the fluid power system decreases steady-state accuracy, and friction in the actuator degrades the transient performance or even causes stick-slip motion at low speeds. Furthermore, the system may exhibit limit cycle (or hunting) due to Stribeck friction and integral action. This paper proposes a robust high precision position control strategy incorporating leakage and friction compensation for EHAs. Quantitative feedback theory (QFT) is applied to design a robust controller that satisfies the prescribed performance specifications without over-design, considering model inaccuracy and system variations. The internal leakage is subsequently compensated based on experimental data instead of incorporating an integrator in the controller; hence, limit cycle is avoided, and response speed is improved. Friction in the actuator is identified based on the LuGre friction model and compensated through an observer in the loop. Friction variation and load fluctuation are considered to be output disturbances to be suppressed by the QFT controller. The QFT controller with leakage and friction compensation scheme is verified through experiments on a typical EHA. Both the steady-state and transient position tracking performances are greatly improved.