Urbanization has shaped a dynamic relationship between urban grey and green spaces, and this relationship will profoundly affect the stability and sustainability of the urban system. However, few studies have focused on the complex dynamics, spatial patterns, and dominant factors of the coordination between urban grey and green spaces. Therefore, this study develops a grey-green space trade-offs indicator (GGSCI) to assess the dynamic relationship between vegetated and non-vegetated areas during the growth of urban built-up areas. The GGSCI is implemented to evaluate the long-term dynamics of urban growth across 121 cities in the arid zone of northern China (ANC) from 1990 to 2020. We use Mean-Kendall trend analysis methods to capture the typical features of urban greening, and an interpretable machine learning model is combined to reveal the relative contributions of socioeconomic and natural environment indicators to the GGSCI. The results indicate that: the built-up area of ANC has expanded by 5.72 times from 1990 to 2020. Total grey space growth is 2.12 times that of green space. In addition, the relationship between grey and green spaces in ANC is moving from imbalance to balance, with the percentage of cities in imbalance dropping from a maximum of 23.28 % to 0 %. The trend of greening in urban centers is remarkable. We also reveal that socioeconomic and natural environment alternated as the dominant factors influencing changes in the GGSCI at different stages of urbanization, with AAP and NL contributing the most at 22.24 % and 20.21 %, respectively.