The　control　problem　of　coordinated　motion　of　a　free-floating　space　rigid　manipulator　with　external　disturbance　is　discussed.　By　combining　linear　momentum　conversion　and　the　Lagrangian　approach,　the　full-control　dynamic　equation　and　the　Jacobian　relation　of　a　free-floating　space　rigid　manipulator　are　established　and　then　inverted　to　the　state　equation　for　control　design.　Based　on　the　terminal　sliding　mode　control　(SMC)　technique,　a　mathematical　expression　of　the　terminal　sliding　surface　is　proposed.　The　terminal　SMC　scheme　is　then　developed　for　coordinated　motion　between　the　base＇s　attitude　and　the　end-effector　of　the　free-floating　space　manipulator　with　external　disturbance.　This　proposed　control　scheme　not　only　guarantees　the　existence　of　the　sliding　phase　of　the　closed-loop　system,　but　also　ensures　that　the　output　tracking　error　converges　to　zero　in　finite　time.　In　addition,　because　the　initial　system　state　is　always　at　the　terminal　sliding　surface,　the　control　scheme　can　eliminate　reaching　phase　of　the　SMC　and　guarantee　global　robustness　and　stability　of　the　closed-loop　system.　A　planar　free-floating　space　rigid　manipulator　is　simulated　to　verify　the　feasibility　of　the　proposed　control　scheme.