In order to implement three-dimensional(3D) path tracking control for an underactuated autonomous underwater
vehicle(AUV), based on the theory of nonholonomic system, the characteristics of underactuated control system are analyzed, when vehicle lacks lateral thruster. It is proved that constraints on the accelerations of the underactuated AUV are non-integrable. Path-point tracking controller is designed based on Lyapunov stability theorem and adaptive Backstepping method to attenuate environmental current disturbances. The simulation results show that the designed controller can force underactuated AUV to be asymptotically stabilized to a sequence path points, and the accuracy and robustness are more excellent than that of PID control.