Process simulation is a powerful tool to predict material behaviors under specified deformation conditions, so as to optimize the processing parameters. The equation for flow stress is important to numerically analyze. However, the reported constitutive equations of magnesium alloy are only suitable for processing simulation with strain rate between 0.001-1s-1. In this paper, the strain-stress behavior of AZ31 under warm and high strain rate (>103s-1) condition has been investigated by split Hopkinson pressure bar experiments at elevated temperature. The results show that the influence of the temperature on flow stress is more obvious than that of strain rate; the flow stress decreases with the rise of temperature at a certain strain rate. Based on Johnson-Cook model, the constitutive equation of AZ31 magnesium alloy under warm and high strain rate condition has been given out by fitting the experimental data, which can be applied in process simulation of AZ31 magnesium alloy sheet forming.