The　dynamic　modeling,　the　motion　control　and　flexible　vibration　suppression　of　a　free-floating　space　robot　with　flexible-joints,　bounded　torques,　external　disturbances　and　uncertain　parameters　are　discussed.　The　dynamic　equation　of　the　system　is　established　by　using　the　Lagrange　equation　and　the　linear　and　angular　momentum　conservations　of　the　system.　Based　on　singular　perturbation　theory,　the　system　is　decomposed　into　a　slow　subsystem　and　a　fast　subsystem.　For　the　slow　subsystem,　a　robust　fuzzy　sliding　mode　controller　based　on　hyperbolic　sine　functions　is　designed.　The　controller　does　not　need　to　know　the　accurate　system　model.　It　can　compensate　the　system　rotation　angle　errors　caused　by　the　flexible-joints　and　can　realize　the　desired　motion　trajectories　asymptotic　tracking.　The　hyperbolic　sine　functions　can　reduce　the　control　the　amplitude　of　torques　effectively,　which　makes　the　control　system　more　realistic.　For　the　fast　subsystem,　a　velocity　difference　feedback　controller　is　used　to　suppress　the　vibration　caused　by　flexible-joints　and　thus　guarantees　the　system＇s　stability.　The　simulation　results　prove　the　proposed　hybrid　controller＇s　efficiency.