Space　robot　system　will　play　more　and　more　important　function　in　future　space　activities,　and　its　research　get　the　attention　of　all　parties.　If　ignore　the　existence　of　flexible　joint　in　dynamics　modelling　and　designing　control　method　of　free-floating　space　robot,　it　will　be　seriously　influenced　for　precision　and　stability　of　control　system.　The　dynamics　modeling,　motion　trajectory　tracking　control　design　and　flexible　vibration　suppression　of　free-floating　flexible-joints　space　robot　with　uncertain　parameters　is　discussed.　The　system＇s　dynamic　equations　are　established　by　using　the　linear　momentum　conservation,　angular　momentum　conservation　and　the　Lagrange　equation.　Based　on　the　above　results,　in　order　to　realize　the　motion　trajectory＇s　asymptotic　tracking　of　the　space　robot　and　suppress　the　elastic　vibration　caused　by　the　flexible-joint.　The　system　is　decomposed　into　a　slow-subsystem　and　a　fast-subsystem　using　double　time　scale　decomposition　of　singular　perturbation　theory.　For　the　slow-subsystem,　the　fuzzy　adaptive　non-singular　terminal　sliding　mode　control　scheme　is　designed　to　achieve　the　desired　motion　trajectory＇s　asymptotic　tracking.　Said　control　method　takes　nonsingular　terminal　sliding　mode　manifold,　and　according　to　fuzzy　logic　system　is　employed　to　adaptively　adjust　the　switching　term　of　output　of　the　controller,　consequently,　not　only　conquer　the　limitation　of　uncertainties　of　system　that　should　be　known　in　designing,　but　also　get　rid　of　the　disadvantage　of　sliding　mode　controller　vibration.　For　the　fast-subsystem,　a　velocity　difference　feedback　controller　is　proposed　to　suppress　the　elastic　vibration　caused　by　the　flexible-joint,　guarantee　the　stability　of　the　system.　In　the　simulation,　a　free-　floating　flexible-joint　space　robot　system　with　two　rigid　links　and　two　flexible　joints　is　taken　as　an　example.　Copyright©　(2013)　by　the　International　Astronautical　Federation.