To provide high output forces and to reduce the installation space, the electro-hydrostatic actuator (EHA) usually adopts a fixed-displacement pump and an asymmetric single-rod cylinder. However, comprehensive effects produced by its asymmetric flow, and matched and unmatched uncertainties make it difficult to achieve high-accuracy position control. This paper proposed an integrated sliding mode backstepping control based on extended observer for the asymmetric EHA, compensating the imbalanced flow with pilot-operated check valves. Firstly, flow distribution was analyzed, and its state space equation was established for the asymmetric EHA. Two extended state observer (ESO) was employed to achieve real-time estimating of the unmeasured system states, unmatched and matched disturbance. The backstepping method was used to compensate the matched and unmatched disturbance, and an integrated sliding mode controller was developed to eliminate the static error and to improve the response speed. Theoretical analysis indicates that the controller can guarantee the specified tracking performance for the actuator under time-varying unmatched disturbances, and can make the tracking error asymptotically converge to zero under constant matching disturbances. Finally, the designed EHA and controller were combined to simulate with crane dynamics model in MATLAB/Simscape. The simulation results show that the proposed controller can guarantee the position tracking performance of EHA and possess good disturbance rejection ability.