In this work, an as-rolled AZ31 square bar with c-axis//ND (normal direction) texture was used. Side-rolling and reciprocating torsion were performed to treat the bar. Microstructure evolution and tensile-compressive properties were investigated in detail. Initial rolled AZ31 bar exhibits a large yield asymmetry along the rolling direction (RD). Reciprocating torsion can generate extension twins to introduce twin boundaries and twin-texture. The twin structure can reduce yield asymmetry. However, only limited regions in the rolled AZ31 bar can be twinned during torsion. Pre-side-rolling along the transverse direction (TD) can generate two texture components (c-axis//TD texture and c-axis//ND texture) by introducing profuse {10–12} twins. Such dual texture components help increase the regions which are favorable for twinning during torsion. Finally, combining side-rolling and reciprocating torsion generates hybrid {10–12} twins structure on the entire cross-section, resulting in a remarkably low yield asymmetry. The relevant mechanisms were discussed in detail.