To extrusion AZ31 magnesium alloy plate by the constant-strain-rate extrusion techniques, a new constant-strain-rate die was designed. Constant-strain-rate and traditional extrusion were investigated by finite element software Deform-3D separately. Key field variables, metal flow velocity, effective strain, exit temperature and mean stress, were studied systematically using the two type’s dies, during the extrusion processing. Results show that the uniformity of metal flow velocity, effective strain, exit temperature and mean stress are increased by 13.5%, 43.2%, 7.6% and 13.4%, respectively, by the constant-strain-rate extrusion.The effective strain of the plates at the exit of two kinds of dies exhibits gradually increasing trend from the center to the edge and the exit temperature field exhibits a trend that the center keeps stable and the edge gradually reduces. Moreover, the plate at the exit of constant-strain-rate die exhibits lower temperature increment than the plate at the exit of the traditional die. The range of tensile stress of the plate near the die exit is reduced by using constant-strain-rate die and the plate at the exit of constant-strain-rate die exhibit large compressive stress than the plate at the exit of the traditional die.