Since the discovery of the first metallic glass (MG) in 1960, vast efforts have been devoted to the understanding of the structural mechanisms of unique properties, in particular, mechanical properties in MGs, which is helpful for the applications of such novel alloys. As is well known, the cooling rate during the quenching as well as the sample size, significantly affects the mechanical properties in MGs. In order to study the effect of cooling rate on microstructure and deformation behavior in MG by excluding the size effect, Zr₄₈Cu₄₅Al₇ ternary composition with good glass-forming ability is selected as a research prototype in this work. The classical molecular dynamics simulation is utilized to construct four structural MG models with the same size under different cooling rates, and the uniaxial compressive deformation for each model is also simulated. It is found that an MG model prepared at a lower cooling rate has a higher yield strength and is more likely to form shear bands that lead the strain to be localized, resulting in a lower plasticity. The Voronoi tessellation, together with atomic packing efficiency and free volume algorithms that have been designed by ourselves, is used to analyze the four as-constructed models and high-temperature liquid model. It is found that the as-constructed model, which is prepared by quenching metallic melt at a higher cooling rate, can preserve more structural characteristics of the high-temperature liquid. In other words, the higher cooling rate leads to more clusters with relatively low five-fold symmetry, loose atomic packing and large fraction of free volumes in MG. By calculating the distribution of the free volumes, a new computational approach to detecting liquid-like regions in MG models is adopted. It is found that there are more liquid-like regions in the as-constructed model which is prepared by quenching metallic melt at a relatively high cooling rate. This should be the structural origin of the effect of cooling rate on the deformation behavior, in particular, the yield strength and the plasticity. This work provides an understanding of how the cooling rate during quenching affects the microstructure and deformation behavior, and will shed light on the development of new MGs with relatively large plasticity.