A new series of heavy metal oxide (HMO) glasses in the 10WO(3-x)MoO(3)-(90-x)TeO2, x = 10-40 mol% system have been developed using melt quenching technique to investigate their potentiality for radiation shielding applications. Gamma attenuation parameters such as mass attenuation coefficient (MAC) and half value layer (HVL) were measured in a good transmission geometry. The MACS were then used to calculate effective atomic number (Zell). A HPGe detector was used to detect gamma rays of energies 81 keV, 276 keV, 303 keV, 356 keV and 384 keV emitted through a Ba-133 radioactive source. MACS, HVLs and Zs were also calculated in a continuous energy region. One more relevant gamma shielding parameter, the buildup factor was also estimated for the glass samples in a continuous energy region at different penetration depths. Moreover, the developed glasses were investigated with respect to their shielding ability against fast neutron and charged particle radiation in the light of the calculated ranges for electron, proton and alpha particle interactions and macroscopic removal cross sections for fast neutrons. The results were compared with ordinary concrete and a lead (Pb) based glass sample wherever possible. It was concluded that the 10WO(3)-10MoO(3)-80TeO(2) glass sample showed excellent shielding properties when compared to other glasses as well as concrete and Pb-based shielding glass.