In　this　paper,　the　kinematics　and　dynamics　of　free-floating　space　robot　system　is　analyzed.　The　closed-loop　dynamic　error　equations　considering　uncertainties　for　the　space　robot　is　derived　using　a　PD　type　computed　torque　method.　By　introducing　a　compensating　item　standing　for　system　uncertainties,　using　real　coded　genetic　algorithm　to　improving　its　eliminating　precision,　a　new　compensating　learning　control　method　using　genetic　algorithm　is　presented　in　company　with　its　controller　structure　designed.　Simulation　results　verify　the　efficiency　of　the　control　method.