We have investigated the deformation behavior of a La₅₅Al₂₅Ni₂₀ (at%) metallic glass that has a wide supercooled liquid region of 72 K before crystallization. The glassy solid below the glass transition temperature exhibited non-Newtonian viscosity, and the supercooled liquid revealed a Newtonian viscosity that transferred to the non-Newtonian viscosity with increasing strain rate. The supercooled liquid exhibited a high-strain-rate superplasticity due to the Newtonian viscous flow that has a strain-rate sensitivity exponent (m value) of unity. The metallic glass exhibited large elongations of more than 1000% at strain rates ranging from 10⁻⁴ to 10⁰ s⁻¹ and at relatively low temperatures of about 0.7 T_m, and retained the ductile nature without crystallization even after the deformation. The maximum elongation to failure was about 1800% at a strain rate of 1.7×10⁻¹ s⁻¹ and at 503 K (0.71 T_m) under a flow stress of about 40 MPa. The elongation was restricted by the transition to non-Newtonian viscosity and crystallization. We succeeded in establishing the constitutive formulation of the flow stress in the supercooled liquid region. Its formulation was expressed very well by a stretched exponential function σ_flow=D\dotεexp(H^*⁄RT)[1−exp(E⁄{\dotεexp(H^**⁄RT)}^0.82)]. The superplasticity of the La₅₅Al₂₅Ni₂₀ metallic glass was superior to that of the Zr₆₅Al₁₀Ni₁₀Cu₁₅ metallic glass. The metallic glass, moreover, had many advantages in the superplastic deformation, as compared with superplastic polycrystalline materials.