Strain rate sensitivity index, m plays an important role in plastic deformation at elevated temperature. It is affected by strain rate, temperature, and the microstructure of material. The strain rate sensitivity index has been used as a constant for numerical analysis of plastic forming in specified strain rate and temperature. However, the m is varied as the deformation proceeds at an elevated temperature and a certain strain rate. Thus, in this present study, the m has been characterized for the amount of strain by multiple tensile jump tests of AZ31 magnesium alloy, and the variation of m has been discussed with the microstructural observation before and after the deformation. The experimental results show that the variation of m is dependent on the temperature and strain rate, and grain growth with dynamic recrystallization affect the variation of m.