Abstract: Based on the two factors of energy and curvature, a 2-dimension cellular automata model for simulating grain normal growth was proposed.The model can reflect some important phy sical phenomena on grain normal growth, including the relation of grain growth velocity to temperature and curvature and time invariance of grain size distribution.At the same time, a transition rule of cellular automata time (t_CAS)to real time was put forward.Energy-curvature drove cellular automata modeling normal grain growth in welding heat-affected zone is accomplished in real time.The simulation results correspond well with the rule of grain distribution in welding heat-affected zone.