In order to solve the problems of slow convergence speed,easy divergence and uncertain model in under-driven AUV trajectory tracking,a dual closed-loop control strategy based on finite-time and reduced-order state observer is proposed.According to the principle of time scale,it is divided into position control loop and attitude control loop.The position control loop adopts finite time control method to speed up the convergence of position quantity.The attitude control loop adopts dynamic integral sliding mode based on the reduced-order extended state observer to quickly converge the attitude angle and compensate for the mixed uncertainties.The control effect of AUV trajectory tracking is simulated in 3D simulation environment.The simulation results show that the convergence speed,control accuracy,robustness and tracking effect of the proposed controller are higher than those of conventional trajectory trackers,and it can better meet the trajectory tracking control needs of under-driven AUV.