The apparent activation energy Qc, the applied stress exponent n, and rupture life have been determined from creep test results of AZ31 Mg alloy over the temperature range of 200$^{circ}C$ to 300$^{circ}C$ and the 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 with data acquisition computer. At the temperature of 200$^{circ}C$$~$220$^{circ}C$ and under the stress level of 62.43$~$93.59 MPa, and at around the temperature of 280$^{circ}C$$~$300$^{circ}C$ and under the stress level of 23.42$~$39.00 MPa, the creep behavior obeyed a simple power-law relating steady state creep rate to applied stress and the activation energy fur the creep deformation was nearly equal to that of the self diffusion of Mg alloy including aluminum From the above results, at the temperature of 200$^{circ}C$$~$220$^{circ}C$ the creep deformation for AZ31 Mg alloy seemed to be controlled by dislocation climb but controlled by dislocation glide at 280$^{circ}C$$~$300$^{circ}C$ .And relationship beween rupture time and stress at around the temperature of 200$^{circ}C$$~$220$^{circ}C$ and under the stress level of 62.43$~$93.59 MPa, and again at around the temperature of 280$^{circ}C$$~$300$^{circ}C$ and under the stress level of 23.42$~$39.00 MPa, respectively, appeard as fullow; log$sigma$=-0.18(T+460)(logtr+21)+5.92, log$sigma$ = -0.25(T+460)(logtr+21)+8.02 Also relationship beween rupture time and steady state creep rate appears as follow; ln$dot{ =-0.881ntr-2.45