An　adaptive　controller　is　proposed　for　a　space　robot　system　with　unknown　payload　parameters.　The　dynamic　equations　of　dual-arm　space　robot　system　are　derived　through　the　Lagranian　formulation.　The　obtained　dynamic　equation　can　be　represented　by　a　group　of　inertial　parameters.　Based　on　the　results　and　recognizing　the　payload　parameters　are　unknown,　an　adaptive　controller　is　designed　for　the　robot　system　to　track　the　desired　trajectory.　In　particular,　neither　the　position,　the　velocity　are　required,　nor　the　acceleration　of　the　base.　Finally,　the　numerical　simulation　is　carried　out,　which　confirms　the　controller　proposed　is　feasible　and　effective.