If　flexible　joints　were　ignored　in　dynamic　modeling　and　control　method　design　of　a　free-floating　space　robot,　the　precision　and　stability　of　its　control　system　would　be　influenced　seriously.　Here,　the　dynamic　modeling,　motion　trajectory　tracking　control　design　and　flexible　vibration　suppression　of　a　free-floating　space　robot　with　flexible　joints　uncertain　parameters　were　discussed.　The　system＇s　dynamic　equations　were　established　by　using　the　linear　momentum　conservation,　angular　momentum　conservation　and　Lagrangian　equations.　Based　on　the　above　results,　in　order　to　realize　the　motion　trajectory＇s　asymptotic　tracking　of　the　space　robot　and　to　suppress　its　elastic　vibration　caused　by　flexible-joints,　the　system　was　decomposed　into　a　slow-subsystem　and　a　fast-subsystem　using　the　double-time　scale　decomposition　of　the　singular　perturbation　theory.　For　the　slow-subsystem,　the　fuzzy　adaptive　nonsingular　terminal　sliding　mode　control　scheme　was　designed　to　achieve　the　desired　motion　trajectory＇s　asymptotic　tracking.　For　the　fast-subsystem,　a　velocity　difference　feedback　controller　was　proposed　to　suppress　the　elastic　vibration　caused　by　flexible-joints　and　to　guarantee　the　stability　of　the　system.　In　simulations,　a　free-floating　space　robot　system　with　two　rigid　arms　and　two　flexible　joints　was　taken　as　an　example.　The　simulation　results　verified　the　efficiency　of　the　proposed　method.