In this study, new glass samples with a chemical composition of 40Li2B4O7+xBi2O3+(55–x)ZrO4+5CaWO4 (x = 10, 20, 30, 40, and 50 wt%) were fabricated using the melt quenching-annealing technique. Important neutron shielding parameters, such as the effective neutron removal cross-section, half-value layer, and neutron transmission factor, of all the new glass samples were calculated using the GEANT4 Monte Carlo simulation code. In addition, neutron dose measurements were performed using an 241Am–Be fast neutron source with an activity of 74 GBq and an average neutron energy of 4.5 MeV and a BF3 gaseous neutron detector. The results were compared with those of conventional shielding materials to determine the neutron absorption capabilities of the new glass materials. All the new glass samples were found to have excellent neutron shielding abilities. In particular, the GB5 sample had a high absorption capacity compared to the other samples. These new glass samples may be used as shielding materials in various radiation applications, such as generation of nuclear energy, radiation medicine, and the transport and storage of radioactive wastes.