To study the deformation twins and plastic anisotropy of AZ31 magnesium alloy, based on the plastic constitutive theory of rate-correlated crystals, a magnesium alloy model with different initial textures, including slip and twin deformation mechanisms, was established by the finite element method. Besides, the volume fraction of twin crystals was introduced into the model. The relationship among texture evolution, twins, and mechanical properties during compression was studied. Results show that the plastic behavior of crystal depends largely on the initial texture, and the difference in the initial texture leads to the obvious anisotropy of compression behavior: high axial yield and tensile strength and low radial yield and tensile strength. During the compressive plastic deformation process, with increasing the deformation, the volume fraction of activated twin crystal is increased. In addition, the higher the volume fraction of radial compressive activated twin crystal, the lower the volume fraction of axial compressive activated twin crystal. The points of obvious twin crystal appearance in the simulation coincide with those of stress mutation. When the volume fraction of twin crystal reaches a certain value, the stress suddenly changes, the crystal orientation changes significantly, and the new slip system is activated, reflecting the influence of the coupling of slip and twin crystal mechanisms on the mechanical properties of AZ31 magnesium alloy.