This　paper　discusses　control　problem　of　free-floating　dualarm　space　robot　system　with　unknown　payload　parameters　to　track　desired　trajectory　in　inertial　space,　when　the　attitude　of　base　is　controlled　and　its　location　is　uncontrolled.　Combining　the　relationship　of　the　linear　momentum　conversation　and　the　Lagrange　approach,　the　full-controlled　dynamic　equation　and　the　Jacobian　relation　of　free-floating　dual-arm　space　robot　are　analysed　and　established.　Based　on　the　above　results,　for　the　case　of　free-floating　dual-arm　space　robot　system　with　unknown　payload　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　both　the　base　attitude　and　the　end-　effector　of　dual-arm　space　robot,　so　that　they　can　track　the　desired　trajectory　in　inertia　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.　A　two　planar　dual-arm　space　robot　system　is　simulated　to　verify　the　effectiveness　of　the　proposed　control　scheme.　Copyright　©　2009　by　ASME.