It is well known that controlling the microstructure of most industrial materials is the key to control its mechanical and physical properties. In particular grain growth is very important phenomenon in material science. However, it is very difficult to examine the dynamic solidification microstructure evolution at high temperatures or during deformation processes. Computer simulations have been used as an effective solution for that difficulty. Cellular Automaton (CA) is one of the techniques that have been used to simulate the evolution of grain growth. In this study 2D grain growth simulations of Al-1%Mg alloy was simulated using CA model based on different transition principles. The first is based on low energy principle. In this method the changes of boundary energy value is compared for each cell and then choosing the one that can minimize the energy system to the largest extent. The second method is based on changes of thermal energy that is computed for each grain boundary. The transition only occurs at the highest energy value. The third method is based on starting with a number of random distributed nucleuses within the simulation area with different orientations. At each CA steps these nucleuses will grow into a grain without effecting in the other grains. The morphology and grain kinetics are studied and discussed for each case.