The flexibility of space robot system mainly embodies in arm bar of space robot and hinge joints that connect with each arm bar. Because of the complexity of space robot system structure, previous researchers paid less attention on the system which both have flexible joint and flexible arms. Thus this paper discusses dynamics simulation of flexible joints and flexible arm space robot system, motion control algorithm design and hierarchical points order active inhibition problem of arm and joints double flexible vibration that all under the situation of parameter uncertain. According to momentum and moment of momentum conservation relationship, and also based on Lagrange equations, linear torsion spring and hypothesis modal method, we herein deduce system dynamics model. On the base of it, considering about actual situation that each joint hinge has strong flexibility for space robot practical application, we herein introduce joint flexible compensation controller and combined with singular perturbation technology to decompose the whole system into motor moment power subsystem and flexible arm subsystem with independent time scale. For motor moment power subsystem, we design moment differential feedback controller to inhibit system elastic vibration which caused by joint flexibility. For flexible arm subsystem, we propose an adaptive fuzzy global sliding mode control scheme that based on the concept of virtual force. For using the concept of virtual force, we may achieve the control target that not only tracking expected trajectory, but also inhibiting flexible vibration of flexible arm by only designing a control input. Computer numerical simulation comparison experiment testifies the reliability and availability of this scheme.