This paper addresses the problem of pitch and depth control for a novel deep-sea, high-speed, and heavy-load autonomous underwater vehicle based on the lift principle (LP-AUV). One of the characteristics of an LP-AUV is the use of downward lift to overcome varying residual buoyancy and achieve rapid diving. The pitch angle determines the action direction of the lift force, thus affecting the safety and stability of diving and navigation. Specifically, the main requirement for the controller is accuracy and no overshoot in either the depth or pitch outputs of the system. To offer accurate and reliable control ability, with various speeds and residual buoyancies, unmatched disturbances and the action of lift taken into consideration, a single-neuron controller with self-learning and self-adaptive capabilities is proposed. Based on the Hebb learning rule, a supervised learning rule that can learn not only from the principles of neural networks but also from tuning experience is designed. Hence, the weights of the single-neuron controller can be constantly adjusted online to improve the control performance of the system more rapidly. Simulation results show the robustness and effectiveness of the proposed controller toward external disturbances. Finally, a series of lake tests using the LP-AUV are conducted to validate the proposed method.