An AZ31 Mg alloy sheet with bimodal non-basal texture exhibits good formability at room temperature. However, its initial yield stress (YS) is relatively low during uniaxial tension along the rolling direction (RD) at room temperature, which limits its potential for further application. Recent studies have demonstrated that introducing {10\overline{\mathrm{1}}2} extension twin (ET) through predeformation can improve the mechanical properties of Mg alloy sheets with a basal texture at room temperature. However, the predeformation process for Mg alloy sheets with non-basal texture has rarely been investigated, along with their subsequent plastic deformation behavior at room temperature. Therefore, to investigate the room temperature deformation behavior and microstructure evolution of an AZ31 Mg alloy sheet with bimodal non-basal texture after predeformation, this work exerted a 5% thickness reduction on the sheet via cryogenic rolling. Then uniaxial tension experiments at room temperature and microstructure characterization experiments were conducted to illuminate the effect of predeformation on the mechanical behavior and microstructure evolution of the fabricated sheet. The findings indicate that when loaded along the RD, the YS and fracture elongation (FE) of the predeformed sample are 212.5% larger and 56.9% smaller than those of the non-predeformed sample. When loaded along the transverse direction (TD), the YS and FE of the predeformed sample are 6.7% smaller and 37.9% larger than those of the non-predeformed sample. The difference in YS in the predeformed samples is primarily attributed to easier activation of basal <a> slip in grains with a TD texture component in the TD sample than in grains with a bimodal non-basal texture component in the RD sample. The difference in FE in the predeformed samples is due to the inhibition of the expansion of preexsiting {10\overline{\mathrm{1}}2} ETs in the RD sample, resulting in the early occurrence of {10\overline{\mathrm{1}}1} compression twins (CTs). In comparison, the expansion of preexsiting {10\overline{\mathrm{1}}2} ETs can be effectively performed in the TD sample. Additionally, some {10\overline{\mathrm{1}}1}-{10\overline{\mathrm{1}}2} double twins (DTs) would be activated at the later stage of tensile deformation to sustain and/or accommodate local plastic strain.