This study investigates the individual and combined effects of enhancing the radiation shielding properties of waste concrete using the optimal mix design of two waste material powders of different compositions. Marble (MD) and granite (GD) waste dust were individually utilized as partial replacements for cement at a replacement ratio of 6%. Furthermore, two additional mixes were prepared by incorporating 1% by cement weight of nano alumina (NA) to enhance the microstructure of the studied waste concrete. The MGA-concrete was analyzed using X-ray Fluorescence, Energy dispersive X-ray, X-ray diffraction analysis, transmission electron microscopy, and scanning electron microscope techniques. The radiation shielding assets of the examined Concrete samples, such as the linear attenuation coefficient (μ), half value layer (H1/2), tenth value layer (T1/10), and fast neutron removal cross-section were evaluated using the MCS5 Monte Carlo simulation algorithm and Phy-X software. The results showed that the linear attenuation for the GMN-concretes’ order is CO < MD < GD < NA < MD + NA < GD + NA. The GD + Na concrete sample presents the best neutron performance. The studied GMN-concrete samples provide the best protection against γ-rays and fast neutrons. Lastly, the excellent performance of the mixes of waste Granite, Marble, and Nano-Alumina on ordinary would pave the way for their employment as radiation shielding in various nuclear and medical facilities.