A　Terminal　sliding　mode　control　was　proposed　for　a　free-floating　space　robot.　To　discuss　such　an　under-actuated　flexible-link　flexible-joint　space　robot,　a　free-floating　space　robot　with　one　flexible　link　and　two　flexible　revolute　joints　was　presented.　The　dynamical　Lagrange　equation　was　established　by　the　momentum　conservation.　And　a　singularly　perturbed　model　was　formulated　and　used　for　designing　a　reduced-order　controller,　where　the　system　was　decoupled　into　two　subsystems　(a　flexible　space　manipulator　subsystem　and　a　flexible-joint　fast　subsystem).　A　composite　controller　which　consisted　of　two　control　components　was　proposed.　A　Terminal　sliding　mode　controller　was　proposed　to　control　the　flexible　space　manipulator　subsystem.　A　flexible-joint　fast　controller　was　designed　to　stabilize　the　flexible-joint　fast　subsystem　around　the　equilibrium　trajectory　set　up　by　the　flexible　space　manipulator　subsystem　under　the　effects　of　the　Terminal　sliding　mode　controller.　A　numerical　simulation　was　carried　out,　which　confirmed　the　proposed　controller　is　feasible　and　effective.　The　virtue　of　this　control　scheme　is　that　the　base　linear　position,　the　base　linear　velocity,　the　base　linear　acceleration　need　not　be　measured.　In　addition,　it　is　ensured　that　the　tracking　errors　of　the　manipulator　joints　converge　to　zero　in　finite　time.　©,　2015,　China　Mechanical　Engineering　Magazine　Office.　All　right　reserved.