The deep-sea autonomous underwater vehicle (AUV) is equipment of vital importance for ocean exploration, monitoring, and surveying. With a variable buoyancy system (VBS), AUV can achieve rising, diving, and hovering in the water column. This paper proposes a deep-sea AUV with an oil bladder type hydraulic VBS, which controls the oil flow rate with a proportional valve. However, the implementation of accurate depth control for AUV faces various challenges due to the varying water density with depth, the non-linear feature of the hydraulic system, and the disturbance from sea flows and currents. To tackle these problems, a third-order linear active disturbance rejection controller (LADRC) and its fuzzy adaptive version were designed and implemented in MATLAB/Simulink based on the state-space function of the proposed AUV system. Compared with the conventional PID controller, the simulation results indicate that the proposed LADRC controller shows strong robustness to disturbance, with other advantages including smaller steady-state error, overshoot, settling time, and response time. Moreover, the proposed fuzzy LADRC controller could further decrease the overshoot caused by the increasing target distance. The results prove that the designed depth controllers can meet the control requirements of the proposed deep-sea AUV.