In this study, the neutron shielding properties of high-density polyethylene (HDPE) and HDPE-30(B4C, Sm2O3, and Gd2O3) composites were systematically compared using the MCNP6.2 simulation code. The macroscopic cross-section (MaCS) was calculated at 16 different energies in the thermal, epithermal, intermediate, and fast neutron energy regions. Neutron attenuation rates were determined for thicknesses ranging from 0.01 to 20 cm. Secondary gamma-ray energy-flux distributions from neutron interactions were also analyzed. In the thermal energy region, the HDPE-30Gd2O3 composite showed the highest MaCS and thermal neutron attenuation. In the epithermal energy range, the HDPE-30Sm2O3 composite exhibited the highest MaCS values at specific resonance energies. The HDPE-30B4C composite provided relatively stable shielding performance across both the thermal and epithermal energy ranges. At higher energies, the differences among the composites decreased progressively, and at 2 and 4.5 MeV neat HDPE even slightly outperformed the reinforced composites. Analysis of secondary gamma-ray spectra showed that neat HDPE produced the lowest flux. The HDPE-30B4C composite produced a narrow low-energy spectrum carrying the highest peak flux but the lowest integrated flux among the reinforced composites; HDPE-30Sm2O3 produced an intermediate spectrum between those of B4C and Gd2O3, while HDPE30Gd2O3 produced the highest-energy secondary gamma-ray spectrum. The results indicate that neutron shielding should be evaluated considering both the incident neutron energy spectrum and the secondary gammaray spectrum generated from neutron-matter interactions.