An adaptive fast arctangent non-singular terminal sliding mode controller is proposed for the end trajectory tracking control of the underwater manipulator. Firstly, the dynamic model of the underwater manipulator considering water effects is established based on the Morrison equation. Secondly, combining the characteristics of non-singular terminal sliding mode control and arctangent functions, an fast arctangent non-singular terminal sliding mode controller is designed, and the unknown disturbance of the system is predicted based on the radial basis function neural network. Then, the Lyapunov theory is used to verify that the proposed control method can converge to the desired position in finite time. Finally, the effectiveness of the proposed control method is verified by simulation experiments.