Based　on　a　mutual　mapping　neural　network,　the　inverse　kinematic　control　problem　of　the　free-floating　space　manipulator　system　without　base　control　is　discussed.　With　the　geometrical　relation　and　the　linear,　angular　momentum　conservation　of　the　free-floating　space　manipulator　system,　the　kinematic　equation　of　the　system　is　deduced　and　the　generalized　Jacobian　matrix　is　obtained.　Following　the　above　result,　a　mutual　mapping　neural　network　inverse　kinematic　control　scheme　employing　Lyapunov　functions　is　designed　to　control　the　end-effecter　of　the　free-floating　space　manipulator　system　to　track　the　desired　trajectory　in　workspace.　The　control　scheme　needs　neither　the　structure　of　generalized　Jacobian　matrix　nor　the　relevant　information　of　dynamic　parameters.　A　planar　two-link　free-floating　space　manipulator　system　is　simulated　to　verify　the　designed　control　scheme.