The properties of hybrid nonlinear surface-phonon-plasmon-polaritons (SP3) at the interface of nonlinear medium and graphene-covered hexagonal boron nitride (hBN) are investigated theoretically. It is demonstrated that the hybrid nonlinear SP3 can be tuned by controlling the chemical potential, layer number and relaxation time of graphene. The real and imaginary parts of the propagation constant increase by decreasing the Fermi energy or the layer number of the graphene in the frequency outside of the upper Reststrahlen band of hBN. Moreover, we show that the nonlinear dielectric permittivity has great effect on the propagation constant. The real part of the propagation constant increases with positive nonlinear dielectric permittivity at different frequency for low frequency mode; while the imaginary part of the propagation constant decreases in the upper Reststrahlen band of hBN, keeps nearly constant in the lower band, and increases outside the Reststrahlen band with positive nonlinear dielectric permittivity for low frequency mode.