Deformation asymmetry of magnesium alloys is an important factor on machine design in the automobile industry. Represented by the ratio of compressive yield stress (CYS) against tensile yield stress (TYS), deformation asymmetry is strongly related to texture and grain size. A polycrystalline viscoplasticity model, modified intermediate phi-model, is used to predict the deformation behavior of magnesium alloys with different grain sizes. Validated with experimental results, integrated computational materials engineering is applied to find out the route in achieving desired asymmetry via thermomechanical processing. For example, CYS/TYS in rolled texture is smaller than 1 under different loading directions. In other textures, such as extruded texture, CYS/TYS is large along the normal direction. Starting from rolled texture, asymmetry will increase to close to 1 along the rolling direction after being compressed to a strain of 0.2. Our modified phi-model also shows that grain refinement increases CYS/TYS. Along with texture control, grain refinement also can optimize the yield asymmetry. After the grain size decreases to a critical value, CYS/TYS reaches to 1 because CYS increases much faster than TYS. By tailoring the microstructure using texture control and grain refinement, it is achievable to optimize yield asymmetry in wrought magnesium alloys. Published by Elsevier B.V.