The mass attenuation coefficients (MAC), half–value layers (HVL) and effective atomic numbers (Zeff) of the quaternary tellurite glass system in the form of 75TeO2–15ZnO–(10-x)Nb2O5–xGd2O3, with x= 0.5, 1.0, 1.5, 2.0 and 2.5 mol%, have been investigated at four average medical diagnostic energies (20, 30, 40 and 60 keV) using the chemical compositions and densities reported in various works by other reserachers. The mass attenuation coefficients have been obtained using the FLUKA Monte Carlo code and the results have been shown to be very consistent (with a percentage difference below 1 %) with the values in the XCOM database. Study of the HVL and Zeff have indicated that when the contribution of Gd2O3 in the glass is increased, the HVL decreases and the Zeff increases. Results of the mass attenuation coefficients for the glass samples at 40 and 60 keV have been compared with the ones for commonly used shielding material lead. It has been concluded that at 40 keV, the MAC are comparable with the value for lead. Furthermore, at 60 keV, three of the glass samples with the highest contribution of Gd2O3 have even larger mass attenuation coefficients than that of lead at the same energy.