In this paper, the analytical expressions are derived for the study of Hybrid Surface Phonon-Plasmon-Polaritons (HSP3) in a nonlinear graphene-based structure with hexagonal Boron Nitride (hBN) layers. The numerical results show that the propagation features of HSP3 can be varied by changing the chemical potential, the relaxation time, and the nonlinear coefficient. Due to the existence of hBN layers in the proposed structure, the investigation is done in two frequency ranges: the upper and lower Reststrahlen bands. The obtained results represent that two kinds of hybrid modes propagate outside the upper and lower Reststrahlen bands which we call “higher and lower modes”. However, only one propagating mode is seen inside the upper or lower Reststrahlen band. A high value of FOM=98 is reported at the frequency of 45 THz (inside the upper Reststrahlen band) for the chemical potential of 0.35 eV. The authors believe that the analytical study done on HSP3 in this paper can help the researchers to design innovative structures such as sensors in the mid-infrared region.