This paper solves the path-following control problem of an Autonomous Underwater Vehicle (AUV). Firstly, the path-following error dynamics is established with the concept of path coordinate frame and virtual target, and then transformed into a novel cascade form, which is consist of two subsystems cascaded with the interconnection function, one is position tracking error subsystem and another is surge speed and yaw angle tracking error subsystem, the cascade form decouples the position tracking error subsystem from surge speed and yaw angle tracking error subsystem compared to the traditional solution. Then, command filtered backstepping is adopted to stabilize the surge speed and yaw angle subsystem, which can avoid the complexity and explosion in computing the analytic derivatives of virtual controls, and the filtered tracking errors and input saturation bias are compensated through constructing an auxiliary system with guaranteed bounded stability under Lyapunov theorem. Further, the overall cascade system stability can be proven that all the signals in the closed-loop are uniformly ultimately bounded. Finally, the simulation results are presented to illustrate the effectiveness of the proposed scheme.