Trajectory　tracking　is　a　key　step　for　a　free-floating　space　robot　(FFSR)　system　to　complete　a　space　operation.　However,　the　flexibility　of　links　and　deadzone　in　joint　input　torque　decrease　the　system＇s　trajectory　tracking　accuracy.　The　angle　tracking　for　the　multi-flexible-link　FFSR　was　discussed　to　suppress　the　vibrations　of　the　flexible　links　and　prevent　the　influence　of　the　deadzone.　First,　the　dynamic　equation　of　the　FFSR　system　was　derived.　Second,　the　FFSR　system　was　decomposed　into　the　slow　and　fast　subsystems.　Then,　for　the　slow　subsystem,　a　robust　control　method　based　on　a　nominal　model　and　a　deadzone　estimation　compensator　were　proposed.　For　the　fast　subsystem,　a　linear　quadratic　regulator　optimal　method　was　used　to　actively　suppress　vibrations.　Finally,　experiments　were　carried　out　to　verify　that　the　FFSR　is　capable　of　effectively　tracking　the　desired　trajectory.　The　simulation　results　show　the　robustness　of　the　control　scheme.　It　effectively　suppressed　the　vibrations　as　the　vibration　modes　of　the　links　convergent　to　zero.　This　study　provides　a　control　scheme　for　improving　the　trajectory　tracking　accuracy　of　FFSR,　which　is　of　practical　importance.