This paper addresses the problem of steering autonomous underwater vehicle (AUV) along a desired horizontal path throughout the full-range low-speed and high-speed profiles, experiencing both fully-actuated and under-actuated configurations. First, a nonlinear controller adopting Lyapunov’s direct method and backstepping technique is proposed for under-actuated AUV, based on the Line-of-Sight guidance built in a moving Frenet–Serret frame. And then, the controller is adapted to fully-actuated AUV except that the control computation for the evolution of the side-slip angle is different from the case of under-actuated one. Hence, both the fully-actuated and under-actuated configurations are under the same control framework, which enables a smooth continuous transition between two configurations in a synthesized controller. Finally, simulation results illustrate the performance of the proposed control design, where the varied control efforts in the sway direction clearly show the transitions from fully-actuated to under-actuated configuration.