This　paper　discussed　the　trajectory　tracking　and　vibration　suppression　control　problems　of　free-floating　flexible　space　manipulator　with　an　attitude　controlled　base.　With　the　law　of　conservation　of　momentum,　the　Lagrangian　principle　was　utilized　to　model　the　dynamics　function　of　the　flexible　space　manipulator　incorporating　the　assumed　modes　method.　Using　singular　perturbation　theory,　a　slow　subsystem　describing　the　rigid　motion　and　a　fast　subsystem　corresponding　to　the　flexible　motion　were　obtained.　Then,　a　composite　controller　for　coordinated　motion　between　the　base＇s　attitude　and　the　manipulator＇s　joints　of　flexible　space　manipulator　system　was　designed.　The　slow-subsystem　dual-loop　integral　sliding　mode　controller　dominated　the　trajectory　tracking　of　coordinated　motion　in　the　presence　of　unknown　parameters.　The　fast-subsystem　controller　damped　out　the　vibration　of　the　flexible　link　by　hierarchical　fuzzy　logic　controller.　Numerical　simulation　results　illustrate　that　the　proposed　controller　is　reliable　and　effective.