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Aiming at the problems of slow response speed of underactuated AUV in horizontal plane trajectory, system heavy chattering, big error between trajectory and desired trajectory, the typical AUV movement form, plane trajectory tracking, was researched, the motion law of AUV was analyzed. The level of the error equation was established by converting the ground error variables to hull coordinate variables, underactuated AUV horizontal plane trajectory tracking controller based on backstepping control algorithm was designed, the stability of the closed-loop control system was analyzed by using Lyapunov stability theory. The effectiveness of the designed controller was verified through Matlab numerical simulation, and the stability of tracking algorithm was verified by using backstepping controller designed in trajectory tracking of AUV without interference conditions. The results indicate that the trajectory of the AUV is coincident with the desired curve, the error of horizontal planet horizontal plane trajectory rajectory is controllable, and each index is stable. [ABSTRACT FROM AUTHOR]