The　design　problem　of　a　joint　motion　controller　for　a　flexible-joint　space　robot　with　an　uncontrolled　base　is　discussed.　With　the　linear　and　angular　momentum　conservation　of　the　system　and　a　Lagrangian　method,　the　dynamic　model　of　a　space　robot　is　established.　To　realize　the　control　target　of　joint　motion,　an　adaptive　backstepping　control　scheme　for　a　flexible-joint　space　robot　is　proposed　via　the　function　approximation　technique　of　neural　network.　The　presented　control　scheme　need　not　know　the　information　of　system　parameters,　and　avoids　the　measurements　and　feedback　of　the　position-related　variables　of　the　base.　Thusly,　it　is　more　suitable　for　practical　applications.　Numerical　simulation　results　show　that　the　control　scheme　proposed　can　obtain　the　smaller　vibration　of　flexible　joints　and　effectively　control　the　space　robot　system　to　accomplish　the　desired　joint　motion.