Abstract: Monte Carlo simulations with Potts model were performed to investigate the process of normal grain growth starting from an initial microstructure, the grain size distributions of which could be well described by the Weibull function with a parameter β=3.47. The result show that a parabolic law is observed in grain growth and the simulation time exponent of grain growth n=0.501, which is very close to the theoretical value for grain growth n=0.5, is attained. The complete process of normal grain growth simulation includes transition period and steady state period. In transition period, the grain size distribution is changed rapidly from the Weibull distribution with β=3.47 to the Weibull distribution with β=2.76. In steady state period, the grain size distribution maintains the Weibull distribution with β=2.76. The mean grain face number <f> increases with the increase of time and in the late steady state period <f> approaches soine steady value. The Lognormal function fits the grain face number distribution well and the scope of the individual grain face number is 3-43.