Urban park green space (UPGS) plays an important role in providing ecological and social benefits. However, in many large cities with rapid economic development, the supply of UPGS is unfairly distributed, and there is a severe mismatch between its supply and residents’ demand. Taking the Beijing central city as an example, this study aims to develop a fairness assessment model to quantify the fairness of UPGS distribution and the matching relationships between supply and demand for UPGS. To achieve the aims of the study, we improved the supply model of UPGS by integrating three factors: the number of UPGS, the service capacity of UPGS, and the quality of UPGS in the Beijing central city. Subsequently, we evaluated the spatial fairness and social fairness of the supply of UPGS using the Gini coefficient. Then, we used the number of residents in the sub-district to characterize the intensity of residents’ needs and quantitatively analyzed the spatial matching relationship between the supply of UPGS and residents’ demand. The results show that: (a) The improved supply model of UPGS can measure the supply of UPGS of different types in a more detailed way. (b) The per capita supply of UPGS is unevenly distributed among the six urban districts of Beijing, which may lead to a sense of unfairness among residents. While residents in Haidian District (Gini = 0.649) may have the highest sense of unfairness, followed by those in Fengtai (Gini = 0.505), Dongcheng (Gini = 0.410), Xicheng (Gini = 0.392), and Chaoyang District (Gini = 0.225). (c) The matching relationship between the supply of UPGS and the needs of different social groups is not ideal, especially the spatial matching relationship between the needs of the elderly and the supply of UPGS. This study can be used as a reference for supporting decision making in optimizing UPGS and providing a reference for fine urban management.