This paper addresses the path following problem for an underactuated AUV in three-dimensional space. The path following guidance law is established based on the line-of-sight (LOS) method, and the global integral sliding mode control (GISMC) combined with the backstepping method is used to design the tracking controller. Meanwhile, the adaptive law is designed to eliminate the effects of the parameter perturbation and current disturbance, the stability of the closed-loop system is analyzed based on the Lyapunov stability theory. Finally, simulation results are demonstrated to illustrate the accurate tracking ability and robustness of the proposed controller against the uncertain disturbances.