For the nonlinear parameter-varying (NPV) model of unmanned surface vehicle (USV) with the consideration of the velocities on yaw and surge as well as wave disturbances, a robust H ∞ control method is proposed based on extended homogeneous polynomial Lyapunov function (EHPLF) to regulate heading for the superior performance on the rapidity, accuracy and robustness. Firstly, a NPV model of heading error is established to design a general form of a state feedback controller with a robust H ∞ performance. Secondly, a Lyapunov matrix with full states and varying parameter is constructed to derive the robust H ∞ global exponential stability conditions by Euler’s homogeneity relation for the NPV system, known as the EHPLF stability conditions. Thirdly, since the EHPLF stability conditions consist of a set of nonlinear coupled inequalities that cannot be directly solved by sum of squares (SOS) toolboxes, they are decoupled with matrix transformations to obtain the EHPLF-SOS stability conditions, which is solved for the parameters of the state feedback controller. Finally, the simulation results indicate that EHPLF method exhibits a superior performance on dynamic, steady-state and robustness.