A detailed investigation of the role of titania on gamma and neutron attenuation competence of sodium lead borosilicate 30PbO-20SiO2-(50—y)Na2B4O7 -xTiO2, where y = 0, 10, 20, 30, 40, and 45 mol%) glasses has been evaluated. XCOM and EXABCal softwares have been utilized to achieve the purposes. The increasing (decreasing) in the molar content of TiO2 (Na2B4O7) from 0 (50) to 45 (5) mole % in the glasses subsequently increases the mass density and improves the photon absorbing ability of the glasses. The values of mass attenuation coefficient (MAC) were followed the same trend for all PSNT-glasses throughout the energy spectrum as at maximum (minimum) energy (MAC)PSNT-0 = 39.29 (0.03), (MAC)PSNT-10 = 42.83 (0.031), (MAC)PSNT-20 = 46.91 (0.032), (MAC)PSNT-30 = 51.66 (0.034), (MAC)PSNT-40 = 57.25 (0.035), and (MAC)PSNT-45 = 60.44 (0.036) cm2/g. Linear attenuation coefficient (LAC) values were followed the same trend as MAC values. The effective atomic number (Zeff) were varied from 15.72–61.84 for PSNT-0, 17.00–61.10 for PSNT-10, 18.63–60.41 for PSNT-20, 20.79–59.76 for PSNT-30, 23.81–59.14 for PSNT-40, and 25.81–58.85 for PSNT-45. For most part of the energy spectrum, Zeff(PSNT-45) > Zeff(PSNT-40) > Zeff(PSNT-30) > Zeff(PSNT-20) > Zeff(PSNT-10) > Zeff(PSNT-0). The increasing in the titanium content of the glasses leads to gradual reduction in half value tenth (HVT). The exposure buildup factor (EBF) is noticed to be high at absorption edges and energies where incoherent scattering are high. The fast neutron removal cross-section (FNRCS) of the glasses was 0.0943, 0.0930, 0.0901, 0.0847, 0.0875, and 0.090 cm−1 for PSNT-0, PSNT-10, PSNT-20, PSNT-30, PSNT-40, and PSNT-45, respectively. Generally, the outcome results confirm that the PSNT-45 is the best photon absorber among the PSNT-glasses and the PSNT-0 is the best neutron shielding ability.