Superplasticity describes a material's ability to sustain large plastic deformation in the form of a tensile elongation to over 400% of its original length, but is generally observed only at a low strain rate (~10-4 s-1), which results in long processing times that are economically undesirable for mass production. Superplasticity at high strain rates in excess of 10-2 s-1, required for viable industry-scale application, has usually only been achieved in low-strength aluminium and magnesium alloys. Here, we present a superplastic elongation to 2000% of the original length at a high strain rate of 5 × 10-2 s-1 in an Al9(CoCrFeMnNi)91 (at%) high-entropy alloy nanostructured using high-pressure torsion. The high-pressure torsion induced grain refinement in the multi-phase alloy combined with limited grain growth during hot plastic deformation enables high strain rate superplasticity through grain boundary sliding accommodated by dislocation activity.