Miniature hydraulic actuators are especially suitable for narrow-space and harsh environment arrangement. However, when using thin and long hoses to connect components, the volume expansion caused by pressurized oil inside can have significant adverse effects on the performance of the miniature system. Moreover, the volumetric variation relates to many uncertain factors that are difficult to describe quantitatively. This paper conducted an experiment to test the hose deformation characteristics and presents the Generalized Regression Neural Network (GRNN) to describe the hose behavior. On this basis, a system model of a miniature double-cylinder hydraulic actuation system was established. To decrease the impact of nonlinearity and uncertainty on the system, this paper proposes a Model Predictive Control (MPC) based on Augmented Minimal State-Space (AMSS) model and Extended State Observer (ESO). The extended state space acts as the prediction module model for the MPC, and the disturbance of the ESO estimates is fed to the controller to improve the anti-disturbance capability. The full system model is validated by comparison between the experiment and the simulation. For a miniature double-cylinder hydraulic actuation system, the proposed MPC-ESO control strategy contributes to a better dynamic than conventional MPC and fuzzy-PID. In addition, the position response time can be reduced by 0.5 s and achieves a 4.2% reduction in steady-state error, especially for high-frequency motion. Moreover, the actuation system with MPC-ESO exhibits better performance in suppressing the influence of the load disturbance.