For the nonlinear parameter‐varying (NPV) model of unmanned surface vehicle with the consideration of the velocities on yaw and surge as well as wave disturbances, a robust H∞$$ {H}_{\infty } $$ 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. First, a NPV model of heading error is established to design a general form of a state feedback controller with a robust H∞$$ {H}_{\infty } $$ performance. Second, a Lyapunov matrix with full states and varying parameter is constructed to derive the robust H∞$$ {H}_{\infty } $$ global exponential stability conditions by Euler's homogeneity relation for the NPV system, known as the EHPLF stability conditions. Third, 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.