This paper presents a novel robust fast tube model predictive control (FTMPC) scheme for controlling the multi-input multi-output (MIMO) underwater vehicle-manipulator system (UVMS) in the case of system unmodeled uncertainties and external disturbances. The structure of the FTMPC is designed by a nominal fast MPC and an ancillary tube sliding mode control (SMC) law. The nominal fast MPC uses the approximated prediction control law for achieving the fast online convex optimization. The ancillary tube law uses the explicit SMC for strong robustness and makes the state error between the actual system and the nominal system converge to zero. Finally, the effectiveness of controlling UVMS is verified by the proposed SMC-based FTMPC scheme through the tracking simulations.