An electrohydrostatic actuator (EHA) is a basic mechanical/hydraulic system with deficiencies including significant nonlinearity and parametric uncertainties. In line with the challenges of designing a high-precision control strategy, an adaptive damping variable sliding mode controller is established, which extends our previous work on EHA control. The proposed controller integrates variable-damping sliding mode control, parametric adaptation, and an extended state observer. The parametric uncertainties are effectively captured and compensated by employing an adaptive control law, while system uncertainties are reduced, and disturbances are estimated and compensated with a fast and stable response. We evaluated the proposed control strategy on a variety of position tracking tasks. The experimental results demonstrate that our controller significantly outperforms the widely used methods in overshoot suppression, settling time, and tracking accuracy.