With the growing demands of underwater tasks, trajectory tracking control faces challenges. It must handle model parameter uncertainties, unknown external disturbances, and input saturation. Also, to avoid overestimating tracking error convergence time, the upper convergence time bound needs to be determined beforehand. For a six-degree-of-freedom fully actuated autonomous underwater vehicle, a disturbance observer based non-singular predefined-time control method is proposed. Firstly, a predefined-time disturbance observer is devised for fast and accurate estimation of model uncertainties and external disturbances. Then, based on the pose tracking error, a virtual velocity command is generated using backstepping technique. To address the explosion of computation complexity, a nonlinear first-order filter is adopted to deal with the derivative of virtual velocity command. Meanwhile, an auxiliary dynamic system is introduced. With compensation from the disturbance observer, a non-singular integral sliding mode control law with anti-saturation properties is designed. The Lyapunov theory proves that the closed-loop control system is practically predefined-time stable, so that all signals converge to a neighborhood of the origin. Finally, simulation results verify the effectiveness of the proposed method. It has faster convergence of tracking error than fixed-time control, and the upper convergence time bound is independent of initial states.