To immobilize a high sulfate radioactive wastes a system Na2O-A12O3-P2O5-SO3 has been chosen as one where glasses have a relatively low melting points and good chemical durability. Glasses within partial system 44 Na2O, 20 A12O3 (36-x) P2O5 x SO3 have been prepared at 1000 °C. A possibility of assimilation up to 12 mole % of SO3 has been established. The basic properties of sulfate-containing glasses as density, microhardness, thermal expansion coefficient, transformation and deformation temperatures, viscosity, electric resistivity, leach rate of ions and diffusion coefficients of 22Na, 35S, 90Sr and 137Cs have been measured. Glass structure by infrared and EPR spectroscopies has been investigated.