The　control　problem　of　free-floating　space　robot　system　with　prismatic　joints　was　studied.　In　order　to　overcome　the　difficulty　that　the　dynamic　equation　of　the　system　could　not　be　linearly　parameterized,　the　space　robot　system　was　modeled　as　an　under-actuated　robot　system.　Thus,　the　system　dynamic　equation　can　be　linearly　parameterized.　With　the　momentum　conservation　of　the　system,　the　kinematics　of　the　system　was　analyzed,　and　it　is　shown　that　the　generalized　Jacobi　matrix　can　also　be　linearly　dependent　on　a　group　of　inertial　parameters.　Based　on　the　results　proposed　above,　a　robust　and　adaptive　composite　control　scheme　for　the　end-effector　to　track　the　desired　trajectory　in　inertia　space　was　proposed.　The　control　scheme　avoids　measuring　the　position,　velocity　and　acceleration　of　the　base　with　respect　to　the　orbit,　because　of　an　effective　exploitation　of　the　particular　property　of　the　system　dynamics.　Besides,　the　proposed　control　scheme　is　simple　for　computing,　because　the　controller　is　robust　to　the　uncertain　inertial　parameters.　The　control　scheme　is　verified　in　a　simulation　study.