A　fuzzy　sliding　mode　control　with　simple　structure　and　fast　response　is　proposed　for　the　trajectory　tracking　in　joint　space　of　free-floating　space　manipulators　with　uncertainties　such　as　friction,　external　disturbance　and　unmodeled　dynamics.　In　this　fuzzy　sliding　mode　controller,　the　feedback　linearization　method　is　used　to　equivalent　the　known　part　of　the　dynamics,　then　a　sliding　mode　control　part　is　addressed　to　eliminate　the　uncertainties　of　the　system,　finally　a　T-S　fuzzy　compensation　is　proposed　to　simplify　the　controller　to　reduce　the　computational　burden　and　speed　up　system　response.　The　system　stability　under　this　fuzzy　sliding　mode　controller　is　proved　by　Lyapunov　theory.　The　simulation　comparison　with　nominal　model　based　robust　sliding　mode　control　shows　the　superiority　of　the　proposed　control　method　in　convergence　speed,　response　speed　and　the　performance　of　chattering　elimination.　©　2020,　Springer　Nature　Singapore　Pte　Ltd.