Aiming at the nonlinear characteristics of unmanned surface vehicle(USV) yaw caused by the impact of water flow, a nonlinear parameter-varying(NPV) USV model is established based on yaw motion, and the NPV $H_\infty$ robust heading control method is proposed to improve the rapidity and robustness of heading regulation. Firstly, a nonlinear Fossen model is established based on the hydrodynamic damping by the low aspect-ratio wing theory, which can better describe the characteristics of ship hull impacted by the flow. The dynamics model is simplified into a maneuvering model by ignoring the roll velocity and cross-flow drag, then an NPV heading model is established by introducing the heading. Secondly, a Lyapunov function related to the state of the heading control system and parameter-varying of the surge velocity is constructed to derive the solving conditions of the nonlinear controller, which satisfies the $H_\infty$robust stability of the heading closed-loop control system. This condition is a nonlinear matrix inequality(NLMI). Moreover, since the NLMI is difficult to solve, the nonlinear matrix in the NLMI is replaced with the polynomial matrix based on the sums of squares(SOS) theory to transform into polynomial linear matrix inequalities, which can be solved by SOSTOOLS. Finally, the results of the simulation indicate that the NPV $H_\infty$ controller has fast system response and higher accuracy for heading regulation.