A Zr65Al7.5Ni10Cu17.5-xPdx (x=0-17.5 at. %) alloy system is found to exhibit a different dependence of glass-forming ability (GFA) on atmosphere-pressure during mold casting process. High-Pd alloys (x=7.5-17.5) show a remarkable increase of critical size for glass formation (dc) as casting-atmosphere (Ar) pressure varies from vacuum to ambient. No significant change of dc, however, is observed in low-Pd alloys (x=0-5) despite the variation in atmosphere pressure. The origin of the phenomenon is unveiled by correlating the cooling characteristic during mold casting and on-cooling phase transformation characteristic of the alloy system.