The precision position control for the swashplate servomechanism of the integrated hydraulic transformer (IHT) with mismatched interference is considered in this paper. Compared with the type of port-plate-rotating IHT, the swashplate-rotating IHT has smaller leakage and higher efficiency, but suffers from parameters uncertainty, and time-varying uncertain torque from the plungers. To enhance the robustness of the proposed system, a novel robust control scheme based on a finite-time extended state observer (FTESO) is developed. In the proposed control scheme, the system nonlinearities, parameter uncertainty, actuator failure are both taken into account. And a novel FTESO is established to obtain the state variables, load torque, and failure signals. By introducing the nonsingular terminal sliding mode surface and finite-time technique in each step of the backstepping design, the novel control scheme is able to enhance the robustness of servomechanism and realize finite-time stability of the tracking errors. Finally, the comparative experiment is performed to verify the effectiveness of the controller design.