In order to solve the problem of fast convergence and output error constraint of the system during the Autonomous Underwater Vehicle (AUV) trajectory tracking control, an AUV fast trajectory tracking control algorithm combined Tangential Barrier Lyapunov Function (TBLF) and finite-time control theory is proposed. In view of the disadvantage that the convergence time of traditional asymptotically stable control is uncontrollable, a finite-time controller is designed to ensure that the AUV can realize the fast tracking of designed trajectory in a finite time. Further with TBLF, the trajectory tracking error between true trajectory and desired trajectory of the AUV is constrained to overcome the problem that the traditional Logarithmic Barrier Lyapunov Function (LBLF) can not be applied to the system without error constraint requirements. The simulation results show that the designed control algorithm is of stronger application ability.