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The theoretical calculations on radiation shielding parameters of glass systems in the composition (80-x) B2O3: 20Na2O: xBi2O3 (where x = 0,5,10,15 and 55 mol%) were inquired into using the WinXCom program. The characteristics of radiation shielding parameters for the glass systems had been examined for the mass attenuation coefficients, the effective atomic number, and the electron density in the energy ranges of 1 keV to 100 GeV. These are the glass systems at the different compositions of bismuth which were found that depend upon the energy regions. The results demonstrate that the mass attenuation coefficients, the effective atomic number, and the electron density have the same trend which those values increase with the increasing of the different compositions of bismuth. At the low-energy region, the mass attenuation coefficients show the several discontinuous jumps of the energies which correspond to the photoelectric absorption edges. At the medium-energy region, the Compton scattering process is the main interaction in these energy ranges. In the high-energy regions, pair production becomes the main interaction process and tends to be constant over energy.