To deal with the 3D path-following control problem of underactuated autonomous underwater vehicle (AUV) in the presence of current disturbance and model uncertainty, a tracking error model on the basis of virtual target in Serret-Frenet frame was established. Based on the Lyapunov theory and back-stepping method in kinematic controller, the virtual target with adaptive law and an improved integral line-of-sight (ILOS) guidance law were then developed, which can overcome the interference of current and reduce overshoot. Dynamic controller was designed based on the back-stepping adaptive sliding mode control (BASMC) theory, which guarantees the stability and robustness of the system. Finally, the closed loop stability of the system was demonstrated by the nonlinear cascade system theory. The simulation results demonstrate that the control law, which is implemented based on the relative velocity between AUV and fluid, is convenient for engineering application, and the controller can effectively overcome the influence of current and model uncertainty and realize 3D path-following.