For　the　active　vibration　and　motion　control　of　space　robot　with　multiple　elastic　elements,　a　finite-time　controller　based　radial　basis　neural　network　is　proposed.　First　of　all,　the　dynamic　models　of　the　space　robot　system　with　multiple　elastic　elements　is　derived　by　multi-body　theory.　After　that,　various　singular　perturbation　control　algorithms　are　leveraged　to　the　system　is　decomposed　into　a　slow　subsystem　which　represents　the　rigid　motion　and　a　fast　subsystem　which　represents　the　flexible　links,　elastic　joints　and　elastic　base　vibration.　For　the　slow　subsystem,　a　finite-time　controller　based　on　radial　basis　neural　network　is　designed　to　realize　the　rigid　desired　trajectory　tracking.　For　the　fast　subsystem,　the　linear　quadratic　optimal　control　method　is　adopted　to　suppress　the　vibrations　of　flexible　links,　elastic　joints　and　elastic　base　simultaneously.　The　proposed　control　method　can　realize　active　vibration　suppression,　and　has　good　robustness　and　anti-interference　performance.　Numerical　simulation　verified　the　effectiveness　of　the　proposed　control　scheme.　©　2021　International　Astronautical　Federation,　IAF.　All　rights　reserved.