The　control　problem　of　coordinated　motion　of　a　free-floating　dual-arm　space　robot　with　external　disturbance　is　discussed.　Combined　the　relationship　of　the　linear　momentum　conversation　and　Lagrangian　approach,　the　full-controlled　dynamic　equation　of　a　free-floating　space　robot　with　dual-arms　is　established　and　then　inverted　to　the　state　equation　for　control　design.　Based　on　the　above　results　and　the　terminal　sliding　mode　control　(SMC)　technique,　a　mathematical　expression　of　the　terminal　sliding　surface　is　proposed,　and　then　the　terminal　SMC　scheme　of　coordinated　motion　between　the　base＇s　attitude　and　the　end-effectors　of　the　free-floating　dual-arm　space　robot　with　external　disturbance　is　developed.　This　proposed　control　scheme　not　only　guarantees　the　existence　of　the　sliding　phase　of　the　closed-loop　system,　but　also　ensures　the　convergence　of　the　output　tracking　error　in　a　finite　time　period.　In　addition,　because　the　initial　state　of　the　system　is　always　at　the　terminal　sliding　surface,　the　control　scheme　can　eliminate　the　reaching　phase　of　SMC　and　guarantee　the　global　robustness　and　stability　of　the　closed-loop　system.　A　planar　free-floating　space　robot　with　dual-arms　is　simulated　to　verify　the　feasibility　of　the　proposed　control　scheme.