[Objectives] A non-singular terminal sliding mode control method based on a finite-time disturbance observer is presented for precise tracking control of three-dimensional trajectory of an unmanned underwater vehicle under complex external multidimensional time-varying unknown disturbances. [Methods] Firstly, an error system for position and velocity tracking is established based on the mathematical model of the underwater vehicle. Based on this, a non-singular terminal sliding mode control law is designed, and the power reaching law is used to reduce the chattering of the system while guaranteeing the limited time convergence of the system. Then a finite-time disturbance observer is designed for complex time-varying underwater disturbances. Finally, the stability of the system under this control law is proved by using Lyapunov function. [Results] The results of this paper can provide an effective solution to the precise trajectory tracking problem of unmanned underwater vehicle under complex underwater interference.