In　this　paper,　a　disturbance　observer　based　nonsingular　fast　terminal　sliding　mode　control　(NFTSMC)　scheme　is　proposed　for　the　trajectory　tracking　control　of　an　underactuated　autonomous　underwater　vehicle　(AUV).　A　nonlinear　disturbance　observer　(DO)　is　designed　to　estimate　complex　external　disturbances　and　incorporated　into　a　NFTSMC.　In　constructing　sliding　surfaces,　the　parameter　selection　in　the　exponential　terms　in　NFTSMC　is　expanded.　Lyapunov＇s　second　method　proves　the　uniformly　ultimately　bounded　stability　of　the　proposed　DO　based　NFTSMC.　Simulation　is　performed　to　demonstrate　the　effectiveness　of　the　proposed　controller.　Compared　with　the　existing　NTSMC　methods,　the　convergence　rate　is　improved　by　the　proposed　NFTSMC.　Moreover,　the　proposed　controller　has　good　robustness　to　smooth　external　disturbances.　For　random　disturbances　along　with　an　impulse　at　some　time,　the　proposed　controller　can　also　track　the　disturbance　well　and　achieve　good　robustness.