The square-cylindrical cup of AZ31 Mg alloy with a depth of 50mm and a width of 50 mm was successfully deep drawn from a rolled sheet with a thickness of 0.5 mm using a hydraulic press machine with a capacity of 60 tons. The blank was heated between the die and the blank holder kept in a temperature of 300 degrees C The forming time was about 3 seconds. The fine-grained microstructure was observed at the corner with a sever strain. The grain refinement caused by the dynamic recrystallization contributed to generate high strain-rate superplasticity.