In this paper, we have investigated the properties of tellurite-based glass system in the form (100 -x -y) TeO2-xNbO2.5-yWO3, x = 5, 10, 15, 20, 25 mol% and y = 5 mol% for gamma and neutron shielding applications and to achieve that, mass attenuation coefficients (mu(m)) for the selected glasses have been investigated using Geant4 toolkit and XCOM program, respectively, in the energy range between 1 keV and 10 MeV. A good agreement was observed between mu(m) values simulated by Geant4 and those evaluated by XCOM. The obtained mu(m) values were then utilized to derive effective atomic numbers (Z(eff)), mean free path (MFP), and half value layer (HVL) for the selected glasses. In addition, we used Geometric Progression method (G-P) to evaluate exposure buildup factor (EBF) values in the range of 0.015 MeV-15 MeV up to penetration depths of 40 mfp (mean free path). Among these glasses, the glass coded as TN05W05 is a superior shielding material against gamma-rays as compared with different traditional concretes, commercial glass, and HMO glasses. In addation, the fast neutron removal cross sections were calculated for the glasses involved. It is found that the present glasses offer an excellent ability for protecting against fast neutrons. Present investigation on shielding properties of the selected tellurite-based glasses would be useful for radiation protection application.