This paper examines radiation-shielding abilities of oxyfluoro-tellurite-zinc glasses in the chemical form of AlF3-TeO2-ZnO under the substitution of AlF3 by ZnO. Gamma-ray- and neutron-shielding properties were tested in terms of mass attenuation coefficient (mu/rho), half value layer, mean free path, effective atomic numbers (Z(eff)), effective electron density (N-eff) and removal cross-section (sigma(R)). The mu/rho values of the glasses were generated by Geant4 simulations over an extended energy range and then the generated data were confirmed via XCOM software. The results showed that both gamma-ray- and neutron-shielding efficiencies of the selected glasses evolved by substituting of AlF3 by ZnO. Nuclear radiation-shielding abilities of the current glass systems were compared with that of some conventional shielding materials and newly developed HMO glasses. It can be concluded that oxyfluoro-tellurite-zinc glasses could be useful to design novel shields for radiation protection applications.