Space robots are a kind of coupling system with a rigid body and flexible structures, in which harmonic drive gears are usually used as speed reducers. Thus, the vibration problem is unavoidable due to maneuvering and external disturbances. This paper is concerned with the design and implementation of a fuzzy sliding mode control (FSMC) algorithm and a composite controller to dampen the vibration of a flexible manipulator with a flexible link and a harmonic drive gear (flexible joint). The designed controllers are used to dampen the end-point vibration of the flexible link and flexible joint manipulator, to compensate for unknown and time-varying nonlinear uncertain parameters, such as friction torque and flexible joint characteristics of a harmonic drive gear, etc. The experimental comparison research was conducted, including set-point active vibration control and vibration suppression under resonant excitation. The experimental results demonstrate that the FSMC and the composite algorithms can significantly enhance the performance of vibration suppression for flexible manipulator.