Radiation shielding materials are essential for various applications in space exploration, nuclear power plants, and medical devices. In this study, we present a theoretical design of radiation shielding nanocomposites based on a combination of TiO2-SiO2-Fe3O4-B4C-Al2O3 materials. Using the Phy-X/PSD, EpiXS, and XMuDAT programs, we calculated the radiation shielding properties, including mass attenuation coefficient, mean free path, and effective atomic number, of a series of nanocomposite structures with different Fe3O4 and B4C contents. Our results show that the addition of Fe3O4 and B4C to nanocomposites enhances the radiation shielding efficiency and the maximum shielding is observed in the nanocomposite with the highest density. The theoretical calculations also reveal that the proposed nanocomposites have excellent radiation shielding properties compared to conventional shielding materials, such as lead and concrete. This work demonstrates the potential of using a computational approach to design novel radiation shielding nanocomposites with improved performance, which could have significant implications for a wide range of applications.