Abstract: Urban agglomeration is an important engine leading the development of regional economy. Based on the rank-size rule and allometric growth model of the fractal theory, this paper conducts an empirical study of the urban population evolution rule and the allometric growth rate in the Yangtze River Delta region. The results show that the Ziff dimension of the urban system in the Yangtze River Delta region is close to 1, which suggests that the urban system is relatively sound, and the proportion of cities of different scales is reasonable. At the same time, the allometric growth coefficient of the city group in Yangtze River Delta has a clear reverse changing relationship with the city scale. The allometric growth coefficients of super mega-cities, mega-cities, big cities, medium-sized cities and small cities are 0.41, 0.98, 3.59, 8.19 and 16.7, respectively. That is to say, the larger the city is, the more higher-rise it should be, and the smaller the allometric growth coefficient should be. Therefore, it is necessary, according to the allometric growth coefficient, to control the construction scale and land supply reasonably, to strengthen the rational utilization of resources and environmental protection, to guide the population aggregation scientifically, to optimize the investment environment constantly, to form the characteristic pillar industries, and to promote the economic development level of urban agglomerations in an all-round way.

Key words: city fractal; rank-size rule; allometric growth model; allometric growth coefficient; human-land coordination