A new series of bulk metallic glasses were developed by addition of Fe into the ternary Zr60Cu30Al10 alloy. Although Fe-Cu element pair shows distinct immiscibility with a large positive heat of mixing, substitution of Fe for Cu significantly improves the glass-forming ability of the ternary Zr60Cu30Al10 alloy. The critical diameter for glass-formation increases from 8 mm for Zr60Cu30Al10 alloy to 20 mm for Zr60Cu25Fe5Al10 and Zr62.5Cu22.5Fe5Al10 alloys. As compared with the ternary Zr60Cu30Al10 alloy, the new quaternary Zr-Cu-Fe-Al alloys show lower liquidus temperatures. The Zr60Cu25Fe5Al10 and Zr62.5Cu22.5Fe5Al10 alloys, the best BMG-formers in this alloy system, are found to locate very near a Zr-Cu-Fe-Al eutectic point. The new Zr-Fe-Cu-Al bulk metallic glasses exhibit high strength of about 1700 MPa. The plastic strain increases from 7.8% to 11.3% with increasing the content of Fe from 0 to 12.5%. The finding of a Ni-free Zr-based bulk glassy alloy with the extremely high glass-forming ability is expected to extend the future application of bulk metallic glasses.