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