This work shows the mathematic calculation for obtention of a Cormoran-AUV hydrodynamic model, it also shows a linar control design for a path tracking. The model has been simplified to three degrees of freedom of movement and the whole system has been simulated using Matlab Simulink Software. The system has been linearizated for different velocities to design a linear control for each one of them. However, all resulting systems can be controlled by a unique linear control due characteristics of the vehicle. The designed control is a PD controller, which avoids the position error since the pole of the vehicle model is at the origin. Different paths have been simulated using this control and their results have been comparated in both rising time as establish time.