A robust adaptive heading controller is designed for surface ships considering the internal un-modelled dynamics and the external uncertain disturbances, and the drift angle compensation problem is solved. Based on the second order Nomoto model and the first order drift angle model, the non-integral chain drift angle-heading nonlinear state space model is established, the heading control system un-modelled dynamics and the external uncertain disturbances are considered as a lumped uncertainty, and the unmeasured states and the lumped uncertainty in the model are estimated by a extended state observer(ESO). Based on the Lyapunov stability theory and the adaptive backstepping methodology, the heading state feedback control law is designed. In order to avoid the explosion of complexity problem in the backstepping control process, the derivative of the virtual control signal is approximated by the dynamic surface control technique. The proposed ESO and heading control scheme can ensure all error signals are uniformly ultimately bounded in the closed-loop system, the tracking accuracy is improved in course keeping and course changing processes. Simulation results illustrate the effectiveness of the proposed heading control law.