In the present study, AZ31 Mg-alloy sheets with bimodal non-basal texture were subjected to heating treatment (520^oC/5 h), and then immediately water-quenched and quenched into liquid nitrogen for 12 h. Then, their ambient temperature mechanical performance and microstructure evolution were studied by means of uniaxial tension testing, electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The results show that nano-precipitates Mg₁₇Al₁₂ and Al₈Mn₅ all exist in AZ31 Mg-alloy sheets. However, compared to the Mg-alloy sheet subjected to water-cooling treatment, the volume fraction and size of precipitates increase about 65.5% and 78.7% respectively for the sheet subjected to cryogenic treatment. Meanwhile, the volume fraction of {\mathrm{10}\overline{\mathrm{1}}\mathrm{2}} extension twin (ET) increases by 38.0% and 36.7% for the sheet being subjected to 6% and 12% deformation, respectively. The yield strength (YS) and ultimate tensile strength (UTS) of the cryogenic treated sheets are increased by 43.8% and 5.2%, respectively, compared with the water-cooling treated ones, however, the fracture elongation (FE) decreases by 20.4%. The increase in YS and UTS may mainly be due to the generation of high-density dislocations and precipitation strengthening by Mg₁₇Al₁₂ and Al₈Mn₅ precipitates during cryogenic treatment. The decrease in FE is mainly due to the accumulation of high-density dislocations near {\mathrm{10}\overline{\mathrm{1}}\mathrm{2}} ET boundaries during tensile deformation at room temperature, which would hinder the movement of basal slip and benefit in propagation of microcracks to expand to this region.