The　composite　control　of　coordinated　motion　and　active　vibration　control　for　free-floating　space　flexible　manipulator　with　an　attitude-controlled　base　are　studied.　With　the　momentum　conservation　of　system,　the　kinematics　and　dynamics　of　the　system　are　analyzed　using　Lagrangian　assumed　modes　methods.　It　is　shown　that　the　generalized　Jacobi　matrix　and　dynamic　equations　of　the　system　can　be　linearly　dependent　on　a　set　of　inertial　parameters.　Based　on　the　results　and　under　the　assumption　of　two-time　scale,　singular　perturbation　model　of　the　space　flexible　manipulator　system　is　obtained,　then　the　controller　can　be　designed　separately　to　track　desired　trajectory　and　to　suppress　vibration.　The　fast　subsystem　controller　will　damp　out　the　vibration　of　the　flexible　link　use　an　optimal　Linear　Quadratic　Regulator　(LQR)　method.　The　adaptive　and　robust　composite　control　scheme　of　coordinated　motion　dominates　the　trajectory　tracking　for　both　the　base＇s　attitude　and　tip-position　in　the　slow　subsystem.　The　numerical　simulation　is　carried　out,　which　confirms　the　controller　proposed　is　feasible　and　effective.