The　flexibility　of　the　free-floating　flexible　space　manipulator　system＇s　link　and　joint　may　affect　the　control　accuracy　and　cause　vibrations.　We　studied　the　dynamics　modeling,　joint　trajectory　tracking　control,　and　vibration　suppressing　problem　of　free-floating　flexible-link　and　flexible-joints　space　manipulator　system　with　external　interference　and　uncertain　parameter.　The　system＇s　dynamic　equations　are　established　using　linear　momentum　conservation,　angular　momentum　conservation,　assumed　mode　method,　and　Lagrange　equation.　Then,　the　system＇s　singular　perturbation　model　is　established,　and　a　hybrid　control　is　presented.　For　the　slow　subsystem,　a　robust　fuzzy　sliding　mode　control　is　proposed　to　realize　the　joint　desired　trajectory　tracking.　For　the　fast　subsystem,　a　speed　difference　feedback　control　and　a　linear-quadratic　optimal　control　are　designed　to　suppress　the　vibration　caused　by　the　flexible　joints　and　the　flexible　link　separately.　The　simulation　comparison　experiments　under　different　conditions　are　taken.　The　simulate　results　demonstrate　the　proposed　hybrid　control＇s　validity.　©　The　Author(s),　2021.