The present study established a glass system with composition of 55B2O3 -30Pb3O4-(15 - x) Al2O3- xMoO3, where x: (0≤x≤5 mol %) by melt quenching conventional method. The structure of the synthesized samples was examined by XRD and FT-IR techniques. It is found that the molybdenum acts as a modifier and enhances the change between BO3 and BO4 structural units. Increasing MoO3 in the sample improved the glass network compactness and enhanced the coherence of the glass network and the structure stiffening. Some physical parameters were studied with increasing MoO3 content in the samples such as Ri, ri, rp, dB-B average coordination number, number of bonds, field strength of (Mo+3), the floppy modes, the cross-linking density and effective coordination number and found to be enhanced. Increasing MoO3 dopingconcentration from 0 – 5 mol % produced corresponding increase in fast neutron effective removal cross section ΣR from 0.07127 – 0.10825 cm-1, total cross section for thermal neutrons σT from 68.35875 – 105.7526 cm-1, and an increment in the cold neutron scattering cross section. Furthermore, the influence of MoO3 doping in the glasses is such that the stopping powers (Sp) and ranges RCSDA /Rp of electrons, proton, alpha particles, and carbon ion follows the trend: (Sp)BPAM-G1 > (Sp)BPAM-G2 > (Sp)BPAM-G3 >(Sp)BPAM-G4 > (Sp)BPAM-G5, and(RCSDA /Rp)BPAM-G1 > (RCSDA /Rp)BPAM-G2 > (RCSDA /Rp)BPAM-G3 > (RCSDA /Rp)BPAM-G4 > ((RCSDA /Rp)BPAM-G5 respectively. On the other hand, the doping produced no noticeable differences in the equivalent atomic number and the exposure buildup factor of the glasses.