In　this　paper,　the　fuzzy　adaptive　control　of　coordinated　motion　and　flexible　vibration　active　control　for　space-based　flexible　manipulator　with　an　attitude-uncontrolled　base　are　studied.　First,　Under　the　conversation　of　the　linear　momentum,　the　kinematics　and　dynamics　of　a　space-based　flexible　manipulator　is　analyzed.　Second,　the　jacobian　relationship　between　end-point　velocity　and　the　general　velocities　is　derived.　Based　on　the　results　and　under　the　assumption　of　two-time　scale,　singular　perturbation　model　of　the　space-based　flexible　manipulator　system　is　obtained.　The　fast　subsystem　controller　will　damp　out　the　vibration　of　the　flexible　link　using　a　optimal　Linear　Quadratic　Regulator　(LQR)　method.　For　the　slow　subsystem,　aiming　at　the　case　of　space-based　flexible　manipulator　system　with　uncertain　parameters,　a　composite　control　scheme　is　designed　on　the　base　of　a　computed　torque　controller　and　a　fuzzy　compensator　to　track　desired　trajectories　in　inertial　space,　i.e.,　balancing　the　effect　of　system　unknown　payload　parameters　on　computed　torque　controller　with　fuzzy　adaptive　compensator,　in　order　to　ensure　the　whole　closed-loop　control　system　asymptotic　stability　with　the　existence　of　unknown　payload　parameters.　The　mentioned　control　scheme　can　effectively　overcome　the　effect　of　system　unknown　payload　parameters　and　control　end-effector　of　space-based　flexible　manipulator,　so　that　they　can　track　the　desired　trajectory　in　inertial　space,　with　obvious　advantages　neither　the　mentioned　control　scheme　needs　to　measure　and　feedback　the　position,　velocity　and　acceleration　of　the　floating　base,　nor　the　mentioned　control　scheme　needs　to　requirements　for　the　dynamic　equations　of　the　system　inertial　parameters　in　linear　function.　The　numerical　simulation　is　carried　out,　which　confirms　the　controller　proposed　is　feasible　and　effective.