In the paper, a robust controller using the back-stepping approach and the time delay estimation(TDE) is proposed for the trajectory tracking of torpedo-shape autonomous underwater vehicles(AUVs). The AUV has several difficult issues to design accurate tracking control: unsatisfaction of matching condition and highly nonlinear dynamics including external disturbances. To overcome the matching condition issues, the proposed controller is designed based on the back-stepping approach, which is a well-known method handling unmatched disturbances effectively and having well-established design procedure. To estimate nonlinear vehicle dynamics including sea currents and external disturbances, the TDE, an efficient estimation method using previous system information, is adopted. Owing simplicity of the TDE, the proposed controller does not need whole vehicle dynamics while requiring only the determination of control gains. The stability analysis of the proposed controller is studied, conducting the guidelines for selection of control gains. Through the simulation results using REMUS model, it is demonstrated that the proposed controller has accurate and robust tracking performance even when a vehicle moves under sea currents and external disturbing forces. • A robust tracking controller is proposed for torpedo-like underactuted AUVs. • The controller is robust against sea currents and external disturbing forces. • Not requring whole vehicle model, the controller is easy to be desiged. • The design guidelines based on the stability analysis are addressed. • The robustness of the controller is demonstrated through simulation with REMUS model. [ABSTRACT FROM AUTHOR]