In　this　paper,　aiming　at　the　case　of　free-floating　space　manipulator　system　with　uncertain　inertial　parameters,　when　the　case　of　the　attitude　of　base　controlled　and　its　location　uncontrolled,　we　discuss　trajectory　tracking　control　of　the　dynamic　models　in　inertia　space.　Combined　the　relationship　of　the　linear　momentum　conversation　and　the　Lagrange　approach,　the　full-controlled　dynamic　equation　and　the　Jacobian　relation　of　free　floating　space　manipulator　are　established.　Base　on　above　results　proposed,　a　composite　scheme　of　a　computed　torque　controller　plus　a　fuzzy　compensator　is　proposed　to　track　desired　trajectories　in　inertial　space.　Namely,　it＇ll　make　up　impact　of　system＇s　unknown　parameters　to　computed　torque　controller　through　fuzzy　adaptive　compensation　system　controller,　to　ensure　the　whole　closed-loop　control　system＇s　asymptotic　stability　with　the　existence　of　unknown　parameters.　The　mentioned　control　scheme　can　effectively　control　both　the　base＇s　attitude　and　the　end-effector　of　space　manipulator　to　track　the　desired　trajectory　in　inertia　space.　It　has　obvious　advantages　that　with　needless　feedback　and　measured　the　position,　velocity　and　acceleration　of　the　floating　base,　at　the　same　time,　no　any　requirements　for　the　dynamic　equations　of　the　system　are　linearly　dependent　on　inertial　parameters.　A　two　planar　space-based　manipulator　system　is　simulated　to　verify　the　proposed　control　scheme.