In　this　paper,　the　kinematics　and　dynamics　of　free-floating　space　robot　system　with　dual-arms　are　analyzed.　Considering　the　Uncertainties　of　the　system,　the　state　function　of　the　space　robot　system　with　dual-arms　is　established.　Using　backstepping　method,　a　new　adaptive　robust　tracking　control　method　using　GCMAC(Gauss　basis　function　Cerebellar　Model　Articu　lation　Controller)　is　proposed.　The　Lyapunov　functions　with　state　tracking　error　and　GCMAC　weight　error　is　constructed,　and　the　neural　networks　weight　turn　laws　is　designed,　which,　together　with　the　robust　adaptive　controller,　can　guarantee　the　output　tracking　error＇s　converging　to　zero　while　the　states　of　the　nonlinear　system　and　the　approximation　errors　of　neural　networks　are　boundded.　The　simulation　verified　the　proposed　controller.