This paper investigates the prescribed performance control problem for underwater robots with disturbance. Firstly, for the disturbance of underwater robots, a disturbance observer is designed, and the disturbance estimation error converges to zero in finite time. Then, a nonsingular fast integration terminal sliding mode controller(NFITSMC) is proposed based on the exponential-type barrier Lyapunov function(E-BLF). The controller can make the tracking error converge to zero in finite time and ensure that the static and dynamic performance satisfies prescribed performance index. Finally, the stability of the control system is proved, and a simulation example is given to illustrate the effectiveness of the proposed methods.