During sea missions, underwater vehicles are often exposed to changes in the parameters of their control systems and subject to external disturbances due to the influences of ocean currents. These issues make the design of a robust controller quite a challenging task. This paper focuses on the design of a nonlinear PID controller, based on a set of saturation functions for trajectory tracking on an underwater vehicle. The main feature of the proposed control law is that it preserves the advantages of robust control and remains easy to fine-tune in real applications. Using the Lyapunov concept, we prove the asymptotic stability of the closed-loop tracking system. The effectiveness and robustness of our proposed controller for trajectory tracking in depth and yaw dynamics is demonstrated through real-time experiments.