The characteristics of the population distribution of China is analyzed based on the method of statistical physics. The results show that in the last 20 years, the total population of China increases roughly exponentially with time and the growth rate is found to be slowing down. The population distribution in provinces, cities or counties follows approximately the same rule: the population distribution changes slowly for small k, while it changes rapidly for large k and the distribution obeys the Zipf's law. This shows that the population distribution of China has self-similarity. A solvable model of migration-driven aggregate growth based on scale-free network is also proposed to simulate the population size distribution of China. It is found that the theoretical results are in good agreement with the realistic data.