The ability to create various compounds has made concrete one of the most suitable materials for constructing radiation shields. In this investigation, hematite and magnetite aggregates were used to replace ordinary aggregate, separately and completely in two stages. Boron carbide was also substituting cement at percentages of 2.5, 5, and 10 by mass. The density test, gamma irradiation with Co 60 and neutron irradiation with Am-Be 241 were performed. According to the results, the replacement of ordinary aggregates with hematite aggregates in concrete, improved the linear attenuation coefficient and macroscopic cross section by 17% and 73%, respectively. These parameters increased by 37% and 105%, respectively, by the use of magnetite aggregates. Moreover, with the addition of a maximum of 10% boron carbide to the concrete, the macroscopic cross-section increased by 120%, however, the linear attenuation coefficient decreased by between 5% and 8%. This means that it is possible to have a suitable attenuation of gamma ray and neutron beams in a single layer of concrete shield simultaneously. In addition, the results of the tests and Monte Carlo simulation were found to have good consistency.