Grain refinement and crystal orientation of magnesium alloy AZ31 under torsion extrusion with a square-hole die are investigated. The optimum temperature and ratio of the die rotation speed to the extrusion speed were clarified, resulting in uniformly distributed fine grains with sizes in the range 1- m over the entire cross section of the worked specimen. The crystal orientation of the specimen was determined by electron backscatter diffraction and compared with that of a conventionally extruded specimen. In the case of torsion extrusion, a very strong <0001> texture was observed along the extrusion axis, especially in the center region of the cross section. In contrast, the <0001> direction of many grains in the conventionally extruded specimen tended to be perpendicular to the extrusion axis.