The rolling textures evolution of AZ31 magnesium alloy sheets is investigated by the eccentric-rolls drawing as a simulated rolling. The eccentric-rolls provides a sheet continuously changing in rolling reduction, and a exact processing temperature is ensured by uniformly heating the free-rotatable rolls together with a test piece in a furnace. The formed textures at the different rolling rates of 10 and 100 mm·⁻¹ showed no significant differences in any temperature and rolling reduction. The double peak texture, which appreciably improves low-temperature formability of this alloy, was obtained under rolling reduction of 22% or above at 423–523 K. On the other hand, at 573 K, the texture was typically concentric circle.