The rational allocation of urban public open spaces (UPOS) is critical for creating a livable urban environment. Traditional Two-Step Floating Catchment Area (2SFCA) models often lack sufficient quantitative analysis regarding the supply of urban public service facilities and population demand. This study, taking the area within Chengdu’s Second Ring Road as an example, proposes a 2SFCA model that integrates both supply and demand improvements to evaluate UPOS accessibility. The accessibility results are further analyzed using hotspot analysis, and blind zone detection. In terms of supply improvements, the model incorporates additional indicators beyond the spatial area of UPOS, including service quality and the diversity of surrounding environmental service functions, to better evaluate the overall attractiveness of UPOS to residents. On the demand side, besides population size, the model incorporates the spatial distribution of residents and differences in social characteristics affecting UPOS demand. Results indicate that the improved 2SFCA model, which considers both the attractiveness of UPOS and residents’ demand, significantly enhances the accuracy of accessibility assessments. There are substantial differences in service quality among UPOS, while the diversity of surrounding environmental service functions remains generally high. UPOS demand follows a “high in the northeast—low in the southwest” spatial pattern. The spatial distribution of UPOS accessibility shows a “high in the west—low in the east” pattern, opposite to the demand distribution, indicating a supply–demand mismatch. UPOS accessibility identifies one hotspot cluster and four cold spot clusters, with large areas showing no significant characteristics. Additionally, 10.58% of the study area remains blind zones, requiring urgent attention. This study offers a more scientific method and framework for research on the spatial layout and supply–demand matching of UPOS.
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