The traditional netcage inspection requires divers to complete, which is inefficient and dangerous. The underwater robot inspection is a way to solve the problem. When the robot is in motion, the camera shoots the netcage, replacing the manual inspection. A new hybrid control strategy based on neural network (NN) and proportional integral differential (PID) is proposed for underwater three‐dimensional path tracking, which overcomes the defect that the traditional feedback regulation can only work after the occurrence of deviation. A feedforward controller based on neural network is designed to predict the disturbance of the controlled object and enhance the anti‐interference ability of the system. Firstly, implement global path tracking based on azimuth and course. Then when the remotely operated vehicle (ROV) deviates from the path, local path planning with rapidly‐exploring random trees (RRT) algorithm. ROV tracks local path and returns to the global path. Finally, using the moving average (MA) algorithm of RRT path smoothing, a smooth path is obtained to minimize ROV jitter, which ensures that the ROV can clearly take pictures of the netcage, and the service life of the ROV is extended. ROV can replace manual inspection, and it only takes about 30 min to rotate a circle, greatly improving work efficiency. The control approach was tested underwater at different depth path tracking scenarios. The experimental results show that in the case of waves <0.5 m, the average tracking error of ROV is <0.5 m, the fluctuation of roll angle and pitch angle is <6°, the average distance error from ROV to mesh netcage is about 0.2 m, and the underwater netcage inspection task is completed stably. [Video attachment: https://youtu.be/NKcgPcej5sI].