Recently, a series of quaternary Zr-based bulk metallic glasses (BMGs), i.e., Zr53Cu18.7Ni12Al16.3, Zr51.9Cu23.3Ni10.5Al14.3 and Zr50.7Cu28Ni9Al12.3, have been developed and their glass-forming ability (GFA) increases with Cu concentration. In this work, atomic structures of the three BMGs were rebuilt by reverse Monte Carlo simulations based on the reduced pair distribution functions measured by high energy X-ray diffraction. The results show that a certain amount of substitution of short Zr-Cu, Cu-Cu pairs with long Zr-Zr and Zr-Al pairs enhances the local denser packing of Kasper polyhedral centered by Zr and Al atoms. A cell sub-divided method is proposed to describe the fluctuation of local number density which is found to follow the normal distribution function. The largest possible free volume in the three alloys is found to approaches to 3.8 Å. For the three alloys, the enhancement of GFA with increasing Cu content is due to the increase in the fluctuation degree of local density instead of the dense packing. © 2009 Elsevier B.V. All rights reserved.