In this work, the melt-quenching process was employed to prepare a new series of B2O3–BaO–Na2O–ZnO–CaO glass systems to explore their radiation-shielding properties. The samples studied were given the following code: G1, G2, G3 and G4. The effect of BaO and ZnO on the ability of the produced glasses to attenuate radiation was studied. The addition of ZnO and BaO led to enhanced glass density. For example, the density of G1, G2, G3, and G4 is 3.017, 3.152, 3.287, and 3.422 g/cm3, respectively. The Phy-X program was employed to study the radiation shielding properties of the glasses in the energy range of 0.122–0.678 MeV, emitted from the Eu-152 radioactive source. According to the results, the glass sample with a composition 52B2O3–11BaO–8Na2O–16ZnO–13CaO (G4) had a higher linear attenuation coefficient (LAC) than the other glasses. For example, the LAC at 0.1218 MeV for G1, G2, G3, and G4 samples is 0.821, 0.996, 1.176, and 1.362 cm−1, respectively. Also, this glass sample possesses a high Zeff due to the high amount of BaO and ZnO. The Zeff values at 0.1218 MeV are 14.217, 16.651, 19.017, and 21.318 for G1, G2, G3, and G4, respectively. The glass sample with the composition of 70B2O3–5BaO–5Na2O–10ZnO–10CaO (G1) has the highest half-value layer (HVL) and mean free path (MFP) among the prepared glasses, meaning the lowest shielding ability compared to other samples. Based on the results, the G4 sample showed the highest shielding properties, making it suitable as a radiation-shielding substance.