In　this　paper,　the　adaptive　neural　network　control　of　space　manipulator　system　is　discussed.　Firstly,　the　dynamic　equations　of　free-floating　space　manipulator　system　are　derived　through　the　Lagranian　formulation.　Based　on　the　above　results,　space　manipulator　system　is　modeled　through　the　neural　network　technique.　And　then　an　adaptive　neural　network　control　scheme　of　space　manipulator　system　with　unknown　parameters　to　track　desired　trajectories　in　joint　space　is　developed.　The　proposed　control　scheme　need　neither　linearly　parameterize　the　dynamic　equations　of　system,　nor　know　any　actual　inertial　parameters.　In　addition,　it　does　not　require　the　time-consuming　training　process　offline　and　saves　the　time　of　neural　network　training.　Lastly,　a　simulation　study　of　a　planar　free-floating　space　manipulator　system　is　presented.　The　simulation　results　show　that　the　proposed　control　scheme　is　feasible　and　effective.