The　dynamics　modelling　and　control　problem　of　space　robot　system　with　flexible-joint　in　inertial　space　are　studied.　Firstly,　the　dynamic　equations　of　the　system　are　established　by　using　of　linear　momentum　conservation,　angular　momentum　conservation　and　the　Lagrange　equation.　Then,　the　system　is　decomposed　into　a　slow　subsystem　and　a　fast　subsystem　base　on　the　singular　perturbation　approach.　For　the　slow　subsystem,　a　fuzzy　variable　structure　sliding　mode　controller　is　proposed.　The　variable　structure　sliding　mode　controller　is　designed　to　achieve　the　asymptotic　tracking　of　the　system.　And　the　fuzzy　controller　is　used　to　overcome　the　chattering　of　the　variable　structure　sliding　mode　controller.　For　the　fast　subsystem,　a　velocity　feedback　control　term　is　used　to　suppress　the　elastic　vibrations　caused　by　the　flexible-joint,　guarantee　the　stability　of　the　system.　The　proposed　control　method　does　not　need　to　measure　and　feedback　the　signal　of　the　base,　so　it　is　simple.　The　simulation　results　show　the　feasibility　and　efficiency　of　the　control　scheme.　Copyright　©2011　by　the　International　Astronautical　Federation.　All　rights　reserved.