This paper addresses the problem of vertical plane path following control of an under-actuated autonomous underwater vehicle (AUV) with a given resultant speed. Different form horizontal plane path following, the AUV moving in the vertical plane is also subject to the restoring torque. In this paper, a consistent guidance and control framework is proposed. In the kinematics guidance layer, an asymptotic pitch guidance law is designed by combining Lyapunov's direct method with Line-of-Sight guidance law built in a moving Serret-Frenet frame. In the dynamics control layer, by considering the effect of angle of attack, a simplified backstepping-based nonlinear controller is derived in order to track the desired resultant speed and the pitch guidance speed generated in the kinematics layer, such that this under-actuated AUV in the vertical plane can track the predefined depth path with a given resultant speed. Finally, the results of numerical simulation are provided to illustrate the effectiveness of the proposed consistent guidance and control framework as well as the designed backstepping-based nonlinear controller.