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-infinity　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-infinity　performance.　Second,　a　Lyapunov　matrix　with　full　states　and　varying　parameter　is　constructed　to　derive　the　robust　H-infinity　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.