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Integration development of urban agglomeration is important for regional economic research and management. In this paper, a method was proposed to study the integration development of urban agglomeration by trajectory gravity model. It can analyze the gravitational strength of the core city to other cities and characterize the spatial trajectory of its gravitational direction, expansion, etc. quantitatively. The main idea is to do the fitting analysis between the urban axes and the gravitational lines. The correlation coefficients retrieved from the fitting analysis can reflect the correlation of two indices. For the different cities in the same year, a higher value means a stronger relationship. There is a clear gravitational force between the cities when the value above 0.75. For the most cities in different years, the gravitational force between the core city with itself is increasing by years. At the same time, the direction of growth of the urban axes tends to increase in the direction of the gravitational force between cities. There is a clear tendency for the trajectories of the cities to move closer together. The proposed model was applied to the integration development of China Liaoning central urban agglomeration from 2008 to 2016. The results show that cities are constantly attracted to each other through urban gravity. [ABSTRACT FROM AUTHOR]