The　dynamics　modeling,　algorithm　design　of　motion　control　and　step　active　suppression　of　joint-　link　double　flexible　vibration　of　free-floating　flexible　space　robot　are　discussed.　The　system　dynamic　equations　are　established　according　to　system　momentum　conservation,　angular　momentum　conservation　and　Lagrange-　assumed　mode　method.　Based　on　singular　perturbation　method,　the　system　is　decomposed　into　a　slow　subsystem　(represents　the　system＇s　rigid　motion),　a　fast　subsystem　1　(represents　the　system＇s　flexible　motion　caused　by　flexible-link),　and　a　fast　subsystem　2　(represents　the　system＇s　flexible　motion　caused　by　flexible-joint).　For　the　slow　subsystem,　a　robust　controller　is　proposed　to　compensate　the　uncertain　parameters　and　rotation　errors,　and　to　realize　the　asymptotic　tracking　of　the　system＇s　motion　trajectory.　For　the　fast　subsystem　1,　linear　quadric　regulator　(LQR)　is　used　to　suppress　the　flexible　vibration　caused　by　flexible-link.　For　the　fast　subsystem　2,　a　feedback　controller　based　on　the　velocity　difference　between　the　link　and　the　motor　is　used　to　suppress　the　flexible　vibration　caused　by　flexible-joint.　So　the　system＇s　controller　is　a　synthesize　controller　by　the　three　controllers.　The　simulation　results　prove　the　controller＇s　efficiency.