Lead borate glasses of the system 25PbO-(75-x) B2O3-xCuO (x = 0, 0.025, 0.05, and 0.1) in mol.% were synthesized via the traditional melt quenching method abbreviated as (BPbCu0, BPbCu1, BPbCu2, and BPbCu3) respectively. XRD diffraction confirmed the amorphous nature of the samples. According to FTIR spectroscopy, the function groups (BO3 and BO4) and the fraction of boron tetrahedral units (N4) were determined. The density, molar volume, packing density, and some other physical parameters were calculated and discussed. The density was increased by incorporating CuO as a substitution for B2O3, while the molar volume was decreased. The ion concentrations of Cu, inter-nuclear distance, field strength, and polaron radius were also computed. The optical absorption study suggested that the copper ions exist in the Cu2+ and act as a modifier by increasing the disorder in the glass network. Hence, the present glass behaves as a bandpass filter in the UV-Vis. region. The radiation shielding properties of the as-prepared samples were theoretically calculated using the Phy-X program at energies ranging from 0.015 to 1.5 MeV. The linear and mass attenuation coefficients, as well as the half-value layer (HVL) and exposure buildup factor (EBF), have been evaluated. The results revealed that shielding parameters are affected by CuO concentrations and photon energy. Based on the results presented in the manuscript, the glass sample with 0.1 mol% CuO doping (BPbCu3) showed the best properties overall for optical and radiation shielding applications. Specifically, BPbCu3 had the highest density, refractive index, optical dielectric constant, and radiation shielding parameters such as linear attenuation coefficient and half value layer among the glass samples. The addition of 0.1 mol% CuO introduced Cu2+ ions which acted as network modifiers, increasing the disorder in the glass structure. This in turn enhanced the optical bandgap as well as the shielding capabilities against gamma radiation.