In this paper, a new controller for an operating manipulator work in the space microgravity environment is proposed. First, on the basis of the load variation caused by microgravity, a sliding mode control method is used to model the gravity term, and the logistic function is introduced as the approaching function. An improved sliding mode reaching law is proposed to control the manipulator effectively, and Lyapunov theory is used to deduce its closed-loop stability. A friction compensation scheme, which regards friction as disturbance, is introduced to the microgravity environment, and a space disturbance observer (SDO) is designed from the viewpoint of disturbance suppression to identify the friction characteristics of the control system accurately. To model the lagging friction phenomenon caused by velocity inversion during operation tasks, an adaptive compensation scheme based on the LuGre model is proposed. Finally, the design of a manipulator system, which consists of a robot arm, dexterous hand, teleoperation system, central controller, and visual system, is presented. On-orbit maintenance and capture experiments are carried out successively. The effectiveness and reliability of the controller are verified, and the on-orbit operation tasks are completed successfully.