Bulk metallic glasses (BMGs) are known to have extraordinary merits such as ultrahigh strength and dynamic toughness etc. but tied to the detrimental brittleness, which has become a critical issue to the engineering application and understanding the glass nature. In this article, we report a new class of Zr-Cu-Al-Mo BMGs with extraordinary plastic strain above 20%. "Work-hardening" effect after yielding in a wide range of plastic deformation process has been detected for this kind of BMGs. Compositional heterogeneity, which can be classified into ZrMo- and Cu-rich zones, was differentiated in this kind of BMG. Pronounced humps have been observed on the high frequency kinetic spectrum in Mo containing BMGs, which is the indicator of β-relaxation transition. The underlying mechanism for the excellent plastic deforming ability of this class of BMGs is ascribed to the synergistic effects of soft ZrMo-rich glass formed through phase separation and abundant flow units which related to β-relaxation.