We present the testing of a high-density magnetite concrete [commercially available under the name Hormirad™, developed by the Spanish company Construcciones Tecnicas de Radioterapia, S.L. (CT-RAD)] as neutron shielding material. The purpose of this work was to characterize the material behavior against neutrons, as well as to test different mixings including boron compounds in an effort to improve neutron shielding efficiency. Hormirad™ slabs of different thicknesses were exposed to a 241Am-Be neutron source under controlled conditions. The original mix, which includes a high fraction of magnetite, was then modified by adding different proportions of anhydrous borax (Na2B4O7). Looking for a comparison, the same experiment was repeated with slabs of ordinary concrete (HA-25) used to shield medical accelerator facilities. In parallel to the experiments, Monte Carlo calculations were performed with MCNP5, with some differences found with regard to the experiments, attributable to uncertainties in the elemental composition of the samples tested. Tenth-value layers have been determined for the different types of concrete tested for the 241Am-Be neutron source. The results show an advantageous behavior of the Hormirad™ when comparing it with ordinary concrete. Although borated concretes show a small improvement in neutron attenuation when they are compared with Hormirad™ alone, the resulting reduction in density and structural properties makes them less practical.