We report a close correlation between the dynamic behavior of serrated flow and the plasticity in metallic glasses (MGs) and show that the plastic deformation of ductile MGs can evolve into a self-organized critical state characterized by the power-law distribution of shear avalanches. A stick-slip model considering the interaction of multiple shear bands is presented to reveal complex scale-free intermittent shear-band motions in ductile MGs and quantitatively reproduce the experimental observations. Our studies have implications for understanding the precise plastic deformation mechanism of MGs.