Equity has been a major concern of urban green space provision. Whether the urban green spaces are equitably provided for socially disadvantaged groups is an important issue in the field of social and environmental justice. This topic is particularly significant in fast-growing Asian countries like China experiencing widening income disparity. This paper examines whether and to what extent the different green spaces (including public parks and urban vegetation) are equitable for all populations (referring to horizontal equity) and also for different social groups (referring to vertical equity) in this typical inland city-Wuhan, China. A novel indicator combining proximity and quality is presented to assess the supply of public parks. The Theil index provides a decomposable measure of overall equity across different regions and vulnerable groups. Both horizontal and vertical perspectives are compared to characterize the spatial equity of urban green spaces (including public parks and urban vegetation) across all population and across different social groups. The empirical analysis of the inland city showed that the overall supply of public parks is far more unequal than mixed or woody vegetation. The distribution of public parks is more inequitable in the outer area, whereas the distribution of mixed or woody vegetation is more inequitable in the inner area. Furthermore, the geographic detector analysis is employed to investigate the spatial relation between socioeconomic contexts and urban green spaces. The spatial heterogeneity of education and age groups is statistically significant for explaining the distribution of public parks. Meanwhile, population density clearly plays a role in the distribution of both public parks and urban vegetation. Per capita income can explain 26% of the distribution of public parks but is not significantly associated with mixed or woody vegetation. Finally, the vertical equity of urban green space is also examined in this paper that the vulnerable groups in the inner area, such as females, residents with low education, children, and the elder suffer from highly unequal accessibility to parks, whereas the vulnerable group in the outer area, such as the migrants gets unequal access to parks.