In　this　paper,　the　kinematics　and　dynamics　of　a　free-floating　space　robot　system　with　prismatic　joint　are　analyzed,　and　it　is　shown　that　the　Jacobian　matrix　and　the　dynamic　equations　of　the　system　cannot　be　linearly　parameterized.　With　the　augmentation　approach,　we　demonstrate　that　the　augmented　generalized　Jacobi　matrix　and　the　dynamic　equation　of　the　system　can　be　linearly　dependent　on　inertial　parameters.　Based　on　the　results,　the　composite　adaptive　control　scheme　for　a　free-floating　space　robot　with　unknown　inertial　parameters　to　track　the　desired　trajectory　in　workspace　is　proposed,　and　a　two-link　planar　space　robot　system　with　prismatic　joint　is　simulated　to　verify　the　proposed　control　scheme.