The mechanical properties of the AZ31B magnesium alloy sheet processed by repeated unidirectional bending (RUB) with a basal pole tilted in the rolling direction were systematically investigated at different temperatures. Compared with the as-received sheet exhibiting approximately the same average grain size, the fracture elongation increased while the proof stress decreased at room temperature. The initial texture had a significant influence on the mechanical properties at room temperature, while it showed a much weaker effect on the mechanical properties because of the activation of non-basal slips and initiation of dynamic recrystallization during deformation at elevated temperature.