This paper solves the path-following control problem of an autonomous underwater vehicle(AUV). Firstly, the path-following error dynamic is established with the concept of path coordinate frame and virtual target, and then transformed into a novel cascade form, which consists of two subsystems cascaded with the interconnection function, one is a position tracking error subsystem and the other is a surge speed and yaw angle tracking error subsystem, and the cascade form decouples the position tracking error subsystem from the 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, it can be proven that all the signals in the closed-loop are uniformly ultimately bounded. Finally, the simulation results show the effectiveness of the proposed scheme.