The　dynamics　modeling,　motion　trajectory　tracking　control　algorithm　design　and　flexible　vibration　suppression　problem　of　free-floating　flexible-joint　space　robot　with　uncertain　parameters　is　discussed.　Firstly,　the　system＇s　dynamics　is　analyzed　and　the　dynamic　equation　is　formulated　by　incorporating　system＇s　linear　momentum　conservation,　angular　momentum　conservation　and　the　Lagrange　equation.　Then　the　system　is　decomposed　into　a　slow　subsystem　(rigid　motion　part)　and　a　fast　subsystem　(flexible　motion　part)　based　on　singular　perturbation　method.　For　the　slow　subsystem,　an　adaptive　sliding　mode　control　algorithm　is　proposed.　The　algorithm,　which　is　comprised　of　a　sliding　mode　based　equivalent　control,　an　adaptive　control　and　a　PID　feedback　control,　integrates　the　advantages　of　sliding　mode　control,　adaptive　algorithm　and　PID　technology　and　covers　their　shortages　as　well.　It　can　compensate　the　system＇s　rotation　error　and　uncertain　parameters,　improve　the　precision　of　the　control　system.　For　the　fast　subsystem,　a　speed　difference　based　feedback　control　algorithm　is　proposed　to　suppress　the　vibration　caused　by　the　flexible　-joints,　guarantee　the　stability　of　the　system.　Finally,　the　simulation　results　validate　the　efficiency　of　the　proposed　hybrid　control　algorithm.