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In this paper, a finite-time extended state observer-based nonsingular fast terminal sliding mode control (NFTSMC) is proposed for the trajectory tracking of autonomous underwater vehicles (AUVs) with various hydrodynamic uncertainties and external disturbances. First, a proportional–integral velocity variable based third-order fast finite-time extended state observer is designed to estimate the lumped uncertainties and their first derivatives. The concepts of finite-time stability and a new proposition are utilized to prove the finite-time uniformly ultimately boundness of the proposed observer. Then, based on the disturbance estimation, an NFTSMC is developed for AUVs. The inverse tangent function and linear control term are used to provide robustness against estimation error and avoid chattering in the thrusters. The position and attitude trajectories are proved to be fast finite-time stable via the Lyapunov theorem. To verify the theoretical analysis, comparative numerical simulations are provided to demonstrate the effectiveness of the proposed control scheme. • A novel FFTESO is developed to accurately estimate the disturbances. • FFTESO-based NFTSMC scheme is designed to achieve the desired trajectory tracking. • The finite-time stability of the proposed scheme can be guaranteed. • The proposed control scheme ensures fast convergence and less chattering. [ABSTRACT FROM AUTHOR]