Low temperature superplasticity (LTSP) was studied in a fine-grained magnesium alloy AZ31 which was processed by multi-directional forging (MDF) under decreasing temperature conditions. Tensile specimens were cut from MDFed Mg alloy parallel to the final compression axis (CA), and the tensile axis perpendicular to the CA. Tensile tests was carried out at temperatures from 393K to 473K and at various strain rates. Superplasticity appears even at a low temperature of 393K with a stress exponent (n) of about 0.56 and a total elongation of 370%. The relative large stress exponent can be connected with grain coarsening taking place during deformation. The initial texture hardly takes place during deformation. This suggests that grain rotation does not occur during superplasticcity.