A　scheme　of　fuzzy　terminal　sliding　mode　control　was　proposed　for　vibration　suppression　of　a　flexible　space　manipulator　base　position　of　which　was　not　controlled.　The　dynamical　equation　of　the　flexible　space　manipulator　was　derived　by　using　the　assumed　mode　method,　linear　momentum　conservation　of　the　system　and　the　Lagrange　method.　To　solve　the　problems　of　trajectory　tracking　control　and　vibration　suppression　of　the　flexible　space　manipulator,　the　singular　perturbation　approach　was　adopted　to　decompose　the　manipulator　system　into　a　slow　subsystem　and　a　fast　subsystem.　And　then,　the　controller　could　be　designed　separately　for　the　subsystems.　A　fuzzy　terminal　sliding　mode　control　scheme　was　designed　to　control　the　slow　subsystem　and　the　linear　quadratic　regulator　(LQR)　based　on　the　reduced　order　observer　was　proposed　for　the　fast　subsystem.　A　simulation　example　of　flexible　space　manipulator　demonstrates　that　the　control　scheme　not　only　guarantees　that　the　tracking　errors　of　the　base＇s　attitudes　and　arm＇s　joints　of　the　system　converge　to　zero　in　finite　time,　but　also　weakens　the　chattering　of　the　sliding　mode　controller　and　the　vibration　of　the　flexible　arm　effectively.