A　continuous　non-singular　terminal　sliding　mode　control　based　on　adaptive　time　delay　estimation　of　free-floating　space　robot　is　presented.　First,　to　overcome　degradation　caused　by　traditional　time　delay　estimation　which　has　used　a　fixed　inertial　matrix,　the　adaptive　time　delay　estimation　is　introduced　to　adjust　the　estimation　value.　An　improved　continuous　non-singular　fast　terminal　sliding　mode　control　is　proposed　which　guarantees　the　continuity　of　the　sliding　mode　surface　and　the　non-singularity　of　the　system.　At　the　same　time,　this　controller　improves　the　convergence　speed　of　the　system　when　the　system　state　approaches　the　sliding　mode　surface　whilst　it　improves　the　control　accuracy　of　the　system.　Then　a　suitable　Lyapunov　function　is　selected　for　analysis　to　prove　the　stability　of　the　control　methods.　Finally,　simulation　is　performed　with　matlab　to　verify　the　effectiveness　of　the　control　scheme.　©　2021　Journal　of　Mechanical　Engineering.