In this paper, a robust finite time trajectory tracking control approach is proposed for autonomous underwater vehicle (AUV), which belongs to the class of highly nonlinear, coupled dynamics with motion in 6-degrees-of-freedom (DOF). The finite-time error convergence and robust control task is accomplished by designing a non-singular fast fuzzy terminal sliding mode controller (NFFTSMC) with disturbance estimator for the 6-DOF dynamics of an AUV. The proposed NFFTSMC incorporates a non-singular fast terminal sliding mode controller (NFTSMC) which not only assures faster and finite convergence of the tracking errors to the equilibrium from anywhere in the phase portrait but also eliminates the issue of singularity dilemma appeared in conventional terminal sliding mode controller (TSMC); a fuzzy logic control (FLC) tool is employed to generate the hitting control signal in order to reduce chattering in control inputs, which commonly occur in conventional TSMC, and an estimated uncertainty term to compensate for the un-modeled dynamics, external disturbances, and time-varying parameters. Furthermore to investigate the effectiveness of the proposed method, it has been extended to task space control problem of an AUV - manipulator system (AUVMS) employed for underwater manipulation tasks. Simulation studies confirms the potency of the proposed method. © 2018 Elsevier Ltd