Ni- and Cu-free Zr–Al–Co–Ag bulk metallic glasses (BMGs) with diameters up to 20 mm were synthesized by copper mold casting. The effects of Ag alloying on the superior glass-forming ability (GFA) of Zr–Al–Co–Ag alloys were studied based on the localized atomic structure and crystallization behavior. High-energy synchrotron radiation x-ray diffraction result reveals that Ag addition in Zr–Al–Co system results in a more homogeneous local atomic structure, which could be an origin for the improved GFA of the Zr–Al–Co–Ag alloy. Crystallization products of the Zr–Al–Co–Ag glassy alloy are more complex than those of the Zr–Al–Co glassy alloy. The Zr–Al–Co–Ag BMGs free from highly toxic elements Ni and Cu exhibited a combination of superior GFA, high compressive fracture strength over 2000 MPa, low Young’s modulus of 93 to 94 GPa, and good corrosion resistance in phosphate-buffered solution (PBS), inspiring their potential biomedical applications.