Recent progress in the synthesis of Mg-based metallic glasses (MGs) has allowed them to be considered as potential candidates for biodegradable and bioabsorbable implant materials. In this work, we use the Mg-Zn-Ca system as a representative to investigate the effect of composition on the atomic-level structure and local chemical environment in Mg-based MGs from ab initio molecular dynamics simulations. The results suggest that the short-range order of Mg(95-x)Zn(x)Ca5 (x = 21, 25, 29, and 33) MGs is characterized by Zn-centered icosahedral and icosahedral-like clusters, which show an increasing number and a rising tendency to interpenetrate each other with the enrichment of Zn constituents. A considerable degree of charge transfer between Zn and the surrounding Mg/Ca atoms is observed through electronic structure and bonding character analysis. At Zn-rich compositions, a percolated Zn-Zn network extended throughout the entire sample is formed, upon which the accumulated charges around Zn atoms are associated into a continuous conductivity path. Such results may shed light on the improved corrosion resistance of the Zn-rich Mg-Zn-Ca MGs.