In this study, optimum processing condition of rolled AZ31 Mg alloy was investigated by utilizing processing map and constitutive equation considering microstructure evolution(dynamic recrystallization) occurring during hot-working. A series of mechanical tests were conducted at various temperatures and strain rates to construct a processing map and to formulate the recrystallization kinetics in terms of grain size. Dynamic recrystallization(DRX) was observed to occur at a domain of $250^{circ}C$ and 1/s(maximum dissipation-efficiency region). The effect of DRX kinetics on microstructure evolution was implemented in a commercial FEM code followed by remapping of the state variables. The volume fraction and grain size of deformed part were predicted using a modified FEM code and were compared with those of actual hot forged part. A good agreement was observed between the experimented results and predicted ones.