Severe plastic deformation (SPD) makes it possible to refine grain size in many metallic materials. Recently, we have developed a new SPD process designated the severe torsion straining process (STSP). This process requires no die but one side of a rod is rotated with respect to the other while producing a local heated zone in the rod and cooling both sides of the heated zone. Torsion strain is then introduced in the local heated zone. The STSP can be a continuous process because the rod is moved in the longitudinal direction while introducing torsion strain through the rotation. For grain refinement using the STSP, various factors may affect, which are the rotation speed, moving speed, straining temperature, cooling rate and diameter of the rod. In this study, the STSP is applied to grain refinement of an A5056 Al-Mg commercial alloy and the factors affecting the grain refinement are optimized. STSP was conducted at a temperature in the range from 573K to 723K. Microstructure was observed by optical microscopy, scanning electron microscopy with an orientation imaging system, and transmission electron microscopy. Microscopy observations revealed that the grain size was reduced to similar to 0.9 mu m, when STSP was conducted at 573K with a rotation speed of 10 rpm and moving speed of 50 mm/min. There is a critical ratio of rotation speed to moving speed above which the rod breaks. The grain size tends to be finer as the straining temperature is lower, the cooling rate is faster and the ratio of rotation speed to moving speed is closer to the critical value.