A new series of barium–lead–praseodymium glass samples was successfully synthesized using the conventional melt-quenching technique. The gamma-radiation shielding performance of the prepared glasses was investigated using the Phy-X/PSD software. The radiation attenuation parameters, including the linear attenuation coefficient (LAC), effective atomic number (Zeff), tenth value layer (TVL), effective conductivity (Ceff), and fast neutron removal cross-section (FNRCS), were evaluated over a wide photon energy range of 0.015–15 MeV for five glass compositions containing different concentrations of Pr2O3 while maintaining constant BaO content. The results revealed that the LAC values were significantly higher at lower photon energies, indicating superior attenuation behavior in this region. Among all investigated compositions, the glass containing 0% Pr2O3 and 10% BaO exhibited the highest LAC and Ceff values along with the lowest TVL values, demonstrating excellent radiation shielding capability. The enhanced shielding efficiency was attributed to the presence of high atomic number elements such as barium (Ba, Z = 56) and praseodymium (Pr, Z = 59), which increase the probability of gamma-ray interaction and attenuation. These findings confirm that the incorporation of BaO-rich compositions significantly improves the nuclear radiation shielding effectiveness of the glass system.