The　dynamic　control　problem　for　free-floating　space　flexible　manipulator　with　unknown　parameters　and　external　disturbance　in　joint　space　is　discussed.　With　the　assumed　modes　method,　the　Lagrangian　principle　is　utilized　to　model　the　dynamic　function　of　the　space　flexible　manipulator　with　completely　uncontrolled　base.　Based　on　above,　a　diagonal　recurrent　neural　network　is　used　to　approximate　the　inverse　dynamic　of　space　flexible　manipulator.　A　control　scheme　based　on　diagonal　recurrent　neural　network　is　designed　to　dominate　the　trajectory　tracking　of　joint　motion　and　damp　out　the　vibration　of　the　flexible　link.　The　control　scheme　does　not　specially　design　active　controller　for　flexible　vibration　suppression,　so　requires　no　measurement　and　feedback　of　flexible　vibration　mode,　which　greatly　simplifies　the　controller　structure.　Furthermore,　the　control　scheme　not　only　requires　no　a　priori　knowledge　about　the　accurate　model　and　system　parameters,　but　also　can　overcome　the　affect　of　external　disturbance.　A　numerical　simulation　is　carried　out　to　illustrate　the　validity　and　feasibility　of　the　proposed　control　scheme.　©2012　Journal　of　Mechanical　Engineering.