This paper has focused on the investigation of gamma and neutron attenuation properties of Li2O-B2O3-P2O5-TeO2 glass system. Gamma shielding parameters such as mass attenuation coefficients (mu(m)), effective atomic numbers (Z(eff)), half value layers (HVL), tenth value layers (TVL), mean free path (MFP), effective electron density (Ne), equivalent atomic numbers (Z(eq)) of investigated glass samples have been calculated in a wide photon energy range of 0.02-20 MeV using MCNPX general purpose Monte Carlo code. The calculated results for mass attenuation coefficients were compared with XCOM. In addition, exposure buildup factors (EBF) and energy absorption buildup factors (EABF) of investigated glasses were determined by using the G-P fitting method. The results showed that sample 9 with the highest density had the lowest HVL, TVL and MFP values among the investigated glasses. Moreover, effective removal cross-sections (Sigma(R)) and transmission factors (TFs) have been calculated. The obtained results have shown that the TeO2 additive into glass samples had a positive effect on the nuclear protection performance of the investigated glass samples. It can be concluded that the impact of TeO2 additive for nuclear radiation shielding applications can be further investigated in different types of glass systems.