Abstract: The two-dimensional normal grain growth has been simulated with Monte Carlo method. With a newly modified algorithm, the attained time exponent of grain growth n equals 0.49±0.01,very close to the theoretical value 0.5. By simulating the complete process of normal grain growth, the grain size distribution is found to be initially a gamma distribution, then varies continuously and slowly with time, finally approaches the function proposed by Hillert in 1965 at the quasi steady grain growth stage. The so-called "self-similarity" of the grain size distribution is discussed according to the new simulation results.