This　paper　discusses　the　control　of　a　free-floating　space-based　robot　system　with　time　delay　to　track　the　desired　trajectory　in　inertial　space　when　both　the　attitude　and　location　of　the　base　are　uncontrolled.　Combining　the　relationship　of　the　linear　momentum　conservation　and　the　Lagrange　approach,　the　full-controlled　dynamic　equation　and　the　Jacobian　relation　of　the　space-based　robot　system　are　analyzed　and　established.　Based　on　the　above　results,　for　the　case　of　a　space-based　robot　system　with　time　delay,　mathematical　models　suitable　for　the　design　of　control　systems　under　the　situation　of　time　delay　are　established　by　using　the　Taylor　series　predictive　and　approximation　method.　Using　the　said　mathematical　model,　an　improved　nonlinear　feedback　control　scheme　of　a　space-based　robot　system　with　time　delay　is　proposed.　Meanwhile,　Lyapunov＇s　second　method　is　employed　in　combination　with　the　way　of　norms　and　graphical　analysis　to　prove　the　whole　closed-loop　control　system＇s　asymptotic　stability　with　the　existence　of　time　delay.　The　above　control　scheme　can　effectively　control　the　end-effector　of　a　space-based　robot　to　stably　track　the　desired　trajectory　in　inertial　space.　The　effect　of　the　controllers　is　testified　by　computer　simulation.