The relationship between the twin behavior, the evolution law of texture and the plastic anisotropy of AZ31 magnesium alloy during tensile deformation was studied by combining room temperature uniaxial tensile experiment with crystal plastic finite element through tensile orientation control. Based on the rate-dependent crystal plastic constitutive theory, a plastic constitutive model of crystals with different orientations coupled by slip and twin mechanisms was established, and the effect of twins on the structural evolution and mechanical properties of AZ31 magnesium alloy during plastic deformation was studied by introducing twin crystal integrals. Results show that the specimens with two different orientations show significantly different texture evolution laws during the plastic deformation process, and exhibit obvious anisotropy. When the specimen is axially stretched, the twin is suppressed, and the twin activation volume fraction is low. The twin crystal is easily generated when the specimen is radially stretched, and the twin activation volume fraction is high. The axial specimen has a small shift in the {0001} polar map throughout the plastic deformation process, and the radial specimen has a significant shift in the polar density of the {0001} prismatic surface texture gradually towards the positive and negative directions of RD due to the activation of a large number of tensile twins.