The influence of initial texture on rollability is investigated using cuneal AZ31 Mg alloy sheets. Upon large thickness reduction, the sheet with initial basal texture has many edge cracks, whereas the sheet is crack-free if its normal direction is orthogonal to c-axis of hexagonal close packed (HCP) lattice. Microstructural analysis shows that the former one has heterogeneous grain structure owing to grain-boundary-related recrystallization, and by contrast the later one has a more uniform microstructure for the twin-related recrystallization. The initial nonbasal texture can lead to excellent rollability and anisotropic deformation, based on which a new iterative approach of rolling is proposed, which may achieve large reduction in few passes.