The mechanical behavior and texture evolution of extruded AZ31 magnesium alloy during the axial tension-compression process at room temperature were simulated by a modified viscoplastic self-consistent model considering slip and twin plastic deformation mechanisms. On the basis of EBSD experiment and simulation, the mechanism of tension-compression asymmetry caused by different deformation mechanisms and the texture evolution in the process of plastic deformation were analyzed. Results show that basal slip is the main deformation mode in the early stage of axial tension deformation, but the orientation factor of basal slip is low and has a hard orientation, resulting in higher yield stress. With the increase in strain, prismatic slip becomes the main deformation mechanism, and the strain hardening rate is low, so the stress-strain curve is smooth. In the early stage of axial compression, tension twinning has a high activity due to its low critical shear stress, leading to lower yield stress. As the relative activity decreases rapidly with the tension twinning, the hardening rate increases at the same time. In the later stage, with the activation of compression twinning, its relative activity increases rapidly; the accumulated stress during plastic deformation can be released, and the hardening rate decreases. In addition, the less twin volume fraction in the ED direction was explained by the color and the twin trace of typical grain.