Magnesium alloys have been widely used for many structural components of automobiles and aircraft because of high specific strength and good cast ability in spite of hexagonal closed-packed crystal structure of pure magnesium. In this study, uniaxial tension tests at high temperature and creep tests are done in order to investigate the characteristics of high temperature and mechanisms for creep deformation of AZ31 Mg alloy. Yield stress and ultimate tensile stress decreased with increasing temperature, but elongation increased from results of uniaxial tension test at high temperature. The apparent activation energy Qc, the applied stress exponent n and rupture life have been determined during creep of AZ31 Mg alloy over the temperature range of 473K to 573K and stress range of 23.42 MPa to 93.59 MPa, respectively, in order to investigate the creep behavior. Constant load creep tests were carried out in the equipment including automatic temperature controller, whose data are sent to computer. At around the temperature of $473K{sim}493K$ and under the stress level of $62.43{sim}93.59%MPa$, and again at around the temperature of $553K{sim}573K$ and under the stress level of $23.42{sim}39.00MPa$, the creep behavior obeyed a simple power-law relating steady state creep rate to applied stress and the activation energy for the creep deformation was nearly equal, respectively, and a little low to that of the self diffusion of Mg alloy including aluminum. Also rupture surfaces at high temperature have had bigger dimples than those at lower temperature by SEM.