An evaluation of the gamma-neutron shielding capabilities of polymer nanocomposite materials based on polypropylene and iron nanoparticles is presented in this study. The chemical composition of the materials is (100-x) PP-Fex, (where x = 0.1, 0.3, 0.5, 1, 2 and 5 wt percent). For the proposed polymer samples with photon energies ranging from 30 to 2000 KeV, the mass attenuation coefficient (MAC), a crucial parameter for studying gamma-ray shielding capability, was calculated using the Geant4 Monte Carlo code. Results were compared with those predicted by EpiXS. The values of the Geant4 code and the EpiXS software were both found to be in excellent agreement. Using the mass attenuation coefficient values, we determined the linear attenuation coefficients, electron density, effective atomic number, and half value layer for all the samples. The shielding properties of the polymer samples were also evaluated by estimating both the fast neutron removal cross-section and the mean free path of the fast neutron at energies between 0.25 and 5.5 keV. The study's findings indicate a positive correlation between the Fe nanoparticle content and the gamma-ray shielding performance of PP-Fe polymer samples. Out of the several glasses that were evaluated, it was found that the PP-Fe5 polymer sample demonstrates the highest efficacy in terms of gamma-ray shielding. Moreover, the polymer sample PP-Fe5, which consists of 5 mol% of iron (Fe), exhibits the highest value of ∑R (1.10650 cm-1) and the lowest value of the mean free path for fast neutrons. This indicates that the PP-Fe5 possesses better gamma-neutron shielding efficiency.