Bulk metallic glasses (BMGs), a new class of structural and functional materials with unique physical and chemical features like high corrosion resistance, high yield strength, low elastic modulus, and transparency to visible light indicate they could be the potential shields against unwanted radiations. This study presents an attempt to investigate the radiation shielding efficiencies of a few titanium (Ti)-based BMGs with low densities in the range (4.43 - 5.15) g/cm3. Different shielding properties viz., attenuation coefficients (µm and µ), half and tenth value layers (HVL and TVL), mean free path (λ), effective atomic number (Zeff ), buildup factors (EBF and EABF), and fast neutron removal cross-section (ΣR) were evaluated in the energy range 0.015MeV to 15MeV using Phy-X/PSD software. The five-parametric geometric-progression (G-P) fitting method was employed to calculate EBF and EABF, whereas Zeff values were calculated through the electronic to atomic cross-section ratio. Further, obtained results were compared with two conventional shielding materials: lead (Pb) and heavy concrete (StMg). We found that among 8 BMGs, sample Ti41.9Zr36.3V12.1Cu6.3Be3.4(S1) with the lowest Ti and highest Zr-composition by mass (41.9% and 36.3% respectively) exhibited the best radiation and neutron shielding characteristics with the highest µm (0.02 - 15MeV), µ (0.0015 - 0.2MeV), Zeff (0.015 - 0.06MeV) and ΣR. These values were higher than that of StMg, but lower than those of Pb. Moreover, S1 exhibited the lowest values of HVL, TVL, and MFP in 0.015-0.2MeV region. However, the lowest EBF and EABF values belonged to BMG S1 only in the intermediate energy region (0.1 - 2MeV). But the sample Ti90Al6V4(S7) was the worst among all BMGs and StMg. Thus, low-density Ti-based BMGs have better shielding performances and the potential to replace conventional StMgs and toxic Pb-based materials.