An　adaptive　nonsingular　fast　terminal　sliding　mode　composite　control　algorithm　based　on　wavelet　neural　network　(WNN)　and　hybrid　trajectory　method　is　proposed　for　flexible-base　flexible-joint　and　flexible-link　space　robot　under　the　condition　of　modeling　error　and　external　interference.　The　dynamic　model　of　fully　elastic　space　robot　is　established　by　using　assumed　mode　method,　mass　center　theorem　and　Lagrange　equation.　The　model　is　decomposed　into　slow　and　fast　subsystems　using　singular　perturbation　theory.　The　adaptive　nonsingular　fast　terminal　sliding　mode　control　is　designed　for　the　slow　subsystem,　and　the　double　damping　linear　optimal　control　is　designed　for　the　fast　subsystem.　The　compound　control　algorithm　consists　of　two　sub-controllers.　The　WNN　structure　is　used　to　approximate　the　upper　bound　of　the　system　modeling　error　and　disturbance,　and　the　controller　parameters　are　adjusted　online　by　adaptive　learning　algorithm.　The　simulation　results　show　that　the　composite　controller　can　suppress　the　elastic　vibration　of　the　base,　joints　and　links　within　the　allowable　range　of　±　5　mm,　±　0.1　rad　and　±　1.8　mm　respectively,　it　is　robust　to　modeling　errors　and　external　disturbances,　and　can　realize　the　asymptotic　stable　tracking　of　the　desired　trajectory　within　2　s.　©　2021,　Editorial　Department　of　Journal　of　Chinese　Inertial　Technology.　All　right　reserved.