The　dynamic　modeling,　finite-time　trajectory　tracking　control　and　vibration　suppression　of　a　flexible　two-link　space　robot　are　studied.　Firstly,　the　dynamic　model　of　the　system　is　established　by　combining　Lagrange　method　with　assumed　mode　method.　In　order　to　ensure　that　the　base　attitude　and　the　joints　of　space　robot　can　reach　the　desired　positions　within　a　limited　time,　a　non-singular　fast　terminal　sliding　mode　(NFTSM)　controller　is　designed,　which　realizes　the　finite-time　convergence　of　the　trajectory　tracking　errors.　Subsequently,　for　the　sake　of　suppressing　the　vibrations　of　flexible　links,　a　hybrid　trajectory　based　on　the　concept　of　the　virtual　control　force　is　developed,　which　can　reflect　the　flexible　modes　and　the　trajectory　tracking　errors　simultaneously.　By　modifying　the　original　control　scheme,　a　NFTSM　hybrid　controller　is　proposed.　The　hybrid　control　scheme　can　not　only　realized　attitude　stabilization　and　trajectory　tracking　of　joints　in　finite　time,　but　also　provide　a　new　method　of　vibration　suppression.　The　simulation　results　verify　the　effectiveness　of　the　designed　hybrid　control　strategy.　©　2020　The　Authors