Monte Carlo computer simulations confirmed that an increase in density has a minor effect on the weakening of neutron transport and, therefore, the optimum composition of a shielding concrete against gamma radiation is different than the one against neutron radiation. Neutron radiation shielding is a two-step process: slowing down of fast neutrons and absorption of thermal ones. Both result from the atomic composition of the barrier but their dependence on specified atomic compositions and moisture content is different. The aim of the presented research is to develop a high density concrete the composition of which would also assure good efficiency of neutron shielding. Neutron transport through standard cement mortar, PCC mortar, normal-weight concrete and magnetite heavy-weight concrete has been analyzed in the paper. The goal in research was to find an influence of the cement type, polymer addition, density and moisture content on the shielding properties against neutron. The research based on convergent results of MC computer simulations and real experiments confirmed the influence of the cement type on fast neutron attenuation. It was also found that each 1% of moisture content makes 10% increase of fast neutron thermalization effectiveness, what is a little less than it was estimated for cement based mortars. It was also proved that heavyweight concrete is not proper solution for shielding against fast neutrons, but its efficiency is visible in the case of thermal neutrons absorption, probably due to increase of Fe content at the expense of Si and O in the atomic composition as well as water retained by magnetite aggregate.