Deep inside the ocean, the earth magnetic signal is one of the merely existing information that tells the heading of robots with very good cost efficiency. Therefore, this paper focuses on the AUV (Autonomous Underwater Vehicle) heading control problem using only one magnetic compass as feedback sensor. In this application, we address AUV modeling and control issues simultaneously. Because of quadratic damping factor, underwater vehicle hydrodynamic model is nonlinear. In addition, unmodeled dynamics, parameter variations and environmental disturbances create significant uncertainties between the nominal AUV model and the reality. Finally, sensor noise, signal delay as well as unmeasured states also affect the stability and control performance of AUV motions. In order to handle these issues with improved AUV observation quality and navigation ability, we propose a CFD (Computational Fluid Dynamics) model based H1 robust control scheme.Without loss of generality, the robust heading controller was implemented and validated in the sea on low-mass and complex-shaped Ciscrea AUV. Simulation and sea experimental results of both PID (Proportional Integral Derivative) and robust heading controller are analysed.