The　trajectory　tracking　and　the　double　flexible　vibration　active　suppression　control　for　free-floating　space　robot　with　flexible-joints　and　flexible-link　were　proposed.　The　dynamic　equation　of　the　system　was　established　according　to　system＇s　momentum　conservation　and　Lagrange　method.　A　singular　perturbation　model　was　established　by　integral　manifold　method,　and　the　system　was　decomposed　into　a　fast　subsystem　of　flexible-joint　which　used　the　speed　difference　between　the　feedbacks　of　control　law　to　suppress　the　elastic　vibration　of　flexible-joints,　a　fast　subsystemof　flexible-link　which　designed　optimal　linear　quadratic　regulator　(LQR)　to　damp　out　the　vibration　of　the　flexible　manipulator　and　a　slow　subsystemwhich　designed　a　robust　controller　to　make　the　external　disturbances　have　the　performance　of　the　L　2　-gain　of　the　system,　that　avoids　to　directly　solve　the　HJI　(Inequality　Hamilton-Jacobi)　inequality　of　large　calculation.　Numerical　simulation　results　show　that　the　proposed　control　algorithm　is　effective.　©　2018,　The　Editorial　Board　of　Journal　of　System　Simulation.　All　right　reserved.