The Deep Reinforcement Learning (DRL) algorithm is an optimal control method with generalization capacity for complex nonlinear coupled systems. However, the DRL agent maintains control command saturation and response overshoot to achieve the fastest response. In this study, a reference model-based DRL control strategy termed Model-Reference Twin Delayed Deep Deterministic (MR-TD3) was proposed for controlling the pitch attitude and depth of an autonomous underwater vehicle (AUV) system. First, a reference model based on an actual AUV system was introduced to an actor–critic structure, where the input of the model was the reference target, the outputs were the smoothed reference targets, and the reference model parameters can adjust the response time and the smoothness. The input commands were limited to the saturation range. Then, the model state, the real state and the reference target were mapped to the control command through the Twin Delayed Deep Deterministic (TD3) agent for training. Finally, the trained neural network was applied to the AUV system environment for pitch and depth experiments. The results demonstrated that the controller can eliminate the response overshoot and control command saturation while improving the robustness, and the method also can extend to other control platforms such as autonomous guided vehicle or unmanned aerial vehicle.