In this study, the hot-rolled AZ31 Mg alloy sheet was subjected to dynamic plastic deformation (DPD) with the compression axis taken at different angles to the sheet normal direction (ND). {10-12} twin variant selected is not always the primary one with the highest Schmid factor (SF). For some twinned grains in which the orientations have a deviation of about 10°–40° from the ideal orientation (i.e. rolling direction) favoring {10-12} twinning under compression loading to the DPD direction, the nucleated twin variants have the highest SFs; with higher deviation of 30°–60°, the first twins to form are low-SF variants in the twinned grains. This non-Schmid effect is probably associated with the local-stress fluctuation near grain boundary due to strain accommodation between grains. And the deviation angle that ranged from 30° to 40° is considered to be a transition of variant selection toward the non-Schmid behavior. •Some {10–12} twinning behaviors are not following the Schmid law.•A high deviation of grain orientation from ND results in the non-Schmid twinning behavior.•There is a transition region of {10–12} twinning nucleation toward the non-Schmid behavior.