The　control　problem　of　joint　motion　of　a　free-floating　space　robot　with　dual-arms　was　discussed.　With　the　Lagrangian　approach　and　the　linear,　angular　momentum　conversation,　the　full-controlled　dynamic　equations　of　the　free-floating　space　robot　with　dual-arms　were　derived.　Based　on　the　above　results,　the　free-floating　space　robot　with　dual-arms　was　modeled　by　the　RBF　neural　network　technique,　the　Ge-Lee　(GL)　matrix　and　its　product　operator.　With　all　unknown　inertial　parameters,　the　adaptive　control　scheme　of　joint　motion　of　the　free-floating　space　robot　was　developed　based　on　RBF　neural　network.　This　proposed　control　scheme　needs　neither　linearly　parameterize　the　dynamic　equations　of　the　system　and　knows　any　actual　inertial　parameters,　nor　trains　the　neural　network　offline　so　that　it　could　be　prone　to　real-　time　and　online　application.　The　simulation　results　verify　the　feasibility　of　the　proposed　control　scheme.