In this work, we examined the usefulness of the lithium zinc bismuth borate glass systems for various radiation shielding applications and for this purpose, the mass attenuation coefficients for the glasses in the composition 50 Bi2O3-15 B2O3 (35-x) ZnO (x) Li2O (x = 0, 5, 10, 15, 20 mol%) were calculated by both XCOM software and MCNP5 simulation code, respectively, within the energy range 0.015 MeV-10 MeV. The obtained results indicated good agreement between mass attenuation coefficient values derived from XCOM program and MCNP5 code. The obtained mass attenuation coefficients are then used to calculate the effective atomic number (Zeff), half value layer (HVL) and mean free path (MFP) for the glasses. Among the selected glasses, the glass with 35 mol% ZnO was found to possess superior gamma-ray shielding effectiveness due to its higher values of both mass attenuation coefficient and effective atomic number and lower values of both HVL and MFP. The MFP values of the present glasses were compared with different glass systems and ordinary concrete. In addition, the macroscopic effective removal cross-section for fast neutron (ER) values was also evaluated. It is found that the ER values for the studied glasses lie within the range 0.1286-0.1587 cm(-1).