This paper presents a novel control method of linear oscillating motor in Linear-Driven Electro-Hydrostatic Actuator (LEHA). The tracking accuracy of linear oscillating motor is one of the key factors in the performance of LEHA. During the operation of LEHA, the linear oscillating motor is in the underdamped condition. The equivalent friction damping coefficient is defined in this paper to simplify PID tuning. Velocity and acceleration compensation is proposed here to construct the equivalent friction damping coefficient. In order to increase the oil flow rate in LEHA system, this strategy is combined with the repetitive control method which is capable to improve tracking accuracy. The repetitive controller with damping ratio compensation is also able to realize a high tracking quality under periodic loads.