The primary aim of this investigation is to synthesize a novel glass system with a composition (35+x) PbO-5TeO
2
-20Bi
2
O
3
-(20-x) MgO-20B
2
O
3
(where
x
=0, 5, 10, 15, and 20 mol%) by melt quenching method. The confirmation of the amorphous behavior and the presence of the various vibration modes and stretching modes have been analyzed using the XRD and FTIR techniques, respectively. The radiation shielding parameters of these glasses were reported using MCNP5 simulation. The effects of PbO on the MCNP5 parameters were investigated in detail. The mass attenuation coefficient (MAC) was simulated via MCNP5 code, and it was found that the MAC values from MCNP5 all follow the same trend as the XCOM data. The similarity means that the two simulations strongly agree with each other. The linear attenuation coefficient (LAC) was calculated for all the glasses. The glass sample with 55 mol% of the PbO has the greatest LAC at any energy, such as 0.317 at 10 MeV, the lowest investigated energy. From the LAC values, other parameters such as transmission factor (TF), lead equivalent thickness (
d
lead
), and half-value layer (HVL) were reported. The results for the TF of the glasses revealed that the glass systems become more effective as their thickness increases. Glass sample with 35 mol % of the PbO recorded the highest TF at all energies due to its lack of PbO content, such as 15.533% for a thickness of 1 cm and 6.122% for 1.5-cm thickness at 0.3 MeV. The radiation protection efficiency (RPE) was also determined, and we found that the glasses with the greater PbO content and least MgO content have the highest RPE. Therefore, based on the RPE values, glasses with the greater PbO are the most effective radiation shield from the investigated glasses.