A robust output feedback adaptive control method based on robust observer was proposed based on the fact that the servo-valve controlled elbow joint of a 7-function hydraulic manipulator with double-screw-pair transmission has the control characteristics of strong nonlinearity of the hydraulic system, parametric uncertainties susceptible to temperature and pressure changes of the external environment, unknown external disturbances, and only position and pressure state feedback. The design method of the backstepping controller was utilized to decouple the uncertain system parameters and unknown states. The robust estimator and robust adaptive controller design method were combined to estimate unknown states and uncertain parameters. The globally asymptotic stability and boundedness of system states were guaranteed by using Lyapunov stability theory. Then the robust control problems of coupled uncertain system parameters and partially unknown states were successfully solved. Using the elbow joint of the 7-function master-slave hydraulic manipulator for the 4 500 meter Deep-sea Working System as the research subject, a comparative study was conducted by using the control method under unknown external disturbances. Experimental results show that the close-loop system with strong robustness can track the desired reference trajectory with satisfied dynamic performance and steady accuracy. The modified parameter adaptive laws can also guarantee the boundedness of the estimated parameters.