Near-field thermal radiation (NFTR) between two graphene-covered Si grating (G/Si grating) heterostructures consisting of multilayered G/Si grating cells is investigated, in comparison with that between single-G/Si-grating-cell structures. The calculations are based on the scattering theory utilizing rigorous coupled-wave analysis (RCWA). It is found that strong magnetic polaritons (MPs) can be induced in the single G/Si grating cell, and coupling of multiple MPs can be observed in multilayered G/Si grating heterostructures, which leads to a broader band of high photon-tunnelling probabilities in the phase space. As a result, when the thickness of each grating layer is fixed, the heat flux of the 4-G/Si grating heterostructures, with chemical potential mu = 0.1 eV and grating period L-x = 80 nm, is 1.65- and 9.12-fold larger than those of the 1-G/Si grating and only Si grating structures at d = 100 nm, respectively. When the total thickness of the entire G/Si grating heterostructure is fixed, the 1-G/Si grating model performs better than 2- or 4-G/Si grating models because higher loss inherited from additional graphene sheets would reduce the momenta of the near-unity energy transmission coefficient in the k-space. (C) 2019 Published by Elsevier Ltd.