The　fast　terminal　sliding　mode　fault-tolerant　vibration　suppression　controller　of　the　flexible-base　flexible-link　space　robot　subjected　to　the　actuator　fault　is　designed.　Combing　the　linear　spring　theory,　Euler-Bernoulli　beam　theory　with　the　assumed　mode　method,　the　dynamical　model　of　the　flexible-base　flexible-link　space　robot　is　established　by　using　the　second　Lagrange　equation.　A　finite-time　fault-tolerant　controller　is　proposed　for　the　system　based　on　the　dual-power　non-singular　fast　terminal　sliding　mode,　and　the　stability　of　the　closed-loop　tracking　system　is　proven　through　Lyapunov　function　method.　Then　the　hybrid　trajectory　is　introduced　to　amend　the　finite-time　fault-tolerant　controller,　and　a　dual-power　non-singular　fast　terminal　sliding　mode　finite-time　fault-tolerant　vibration-suppression　controller　on　the　base　of　the　virtual　control　force　is　designed,　which　can　achieve　the　fast　convergences　of　the　tracking　errors　of　the　base　attitude　and　the　manipulator　joints　and　suppress　the　elastic　vibrations　of　the　flexible　base　and　the　flexible　link.　The　simulation　results　show　that　compared　with　the　calculated-torque　vibration-suppression　control　algorithm　which　is　lack　of　the　fault-tolerant　mechanism,　the　error　convergence　rate　of　the　proposed　algorithm　has　increased　by　68.75%　and　the　amplitude　of　the　elastic　base　is　reduced　by　78%,　which　can　be　limited　to　1.1×10-4　m.　©　2023　Editorial　Department　of　Journal　of　Chinese　Inertial　Technology.　All　rights　reserved.