The supply-demand matching of urban park green spaces is directly related to the fairness of urban public services and residents'' livability and well-being. Most existing studies focus on plain cities, and their evaluation systems cannot fully adapt to the characteristics and actual needs of plateau lakeside cities. Therefore, considering multiple natural constraints, including lake-basin landforms, ecological vulnerability, and the scarcity of flat construction land, this paper constructs a coupling coordination evaluation framework for park green space supply and demand that combines spatial service capacity and local geographical endowments. Taking the old-town core area of Kunming as the research case, this paper adopts the improved Gaussian two-step floating catchment area method and entropy weight method to quantitatively analyze the actual supply and demand status of park green space layout. The results indicate three key findings: (1) The supply-demand matching of park green spaces in the study area presents distinct spatial differentiation, showing a pattern of high-level coordination in areas adjacent to mountains and water, and prominent supply-demand imbalance in high-density blocks of the urban core; (2) The coupling coordination degree of supply and demand has a strong correlation with the urban landscape pattern and the distribution of cultural resources; (3) The layout of park green spaces in plateau lakeside cities is restricted by multiple factors, including ecological regulation, spatial constraints from mountains and water systems, prominent compound demands for cultural and tourism functions, and the shortage of land resources. On this basis, this paper puts forward optimization approaches and strategies from three aspects: differentiated zoning regulation, integrated development of blue-green and cultural-green spaces, and intensive utilization of stock space. The research results can provide theoretical reference and methodological support for the equitable allocation, targeted regulation and high-quality coordinated development of park green spaces in plateau lakeside cities during the stock-oriented urban development stage.