In this paper, graphene/h-BN metamaterial was investigated as a new neutron radiation shielding (NRS) material by Monte Carlo N-Particle X version (MCNPX) Transport Code. The graphene/h-BN metamaterial are capable of both thermal and fast neutron moderator and neutron absorber process. The constituent phases in graphene/h-BN metamaterial are chosen to be hexagonal boron nitride (h-BN) and graphene. The introduced target was irradiated by an Am–Be neutron source with an energy spectrum of 100 keV to 15 MeV in a Monte Carlo simulation input file. The resulting current transmission rate (CTR) was investigated by the MCNPX code. Due to concrete’s widespread use as a radiation shielding material, the results of this design were also compared with concrete targets. The results show a significant increase in NRS compared to concrete. Therefore, metamaterial with constituent phase’s graphene/h-BN can be a suitable alternative to concrete for NRS.