Urban parks provide residents with significant cultural ecosystem services (CES) and play a key role in promoting their physical and mental health, contributing to human well-being. With the rapid urbanization in China, many cities have been generally facing the challenges of uneven distribution of urban parks and mismatches of supply and demand in built-up areas. Mountainous cities have unique natural environments that are different from those in plain cities. With the highly dense population, mountainous cities are facing more severe pressure of intense land use, and complex terrain, which may lead to a serious imbalance in the supply and demand of urban parks. This study aims to identify the supply-demand spatial matches and mismatches of cultural ecosystem services (CES) provided by urban parks in polycentric mountainous cities. To do so, we constructed a supply-demand matching assessment framework by taking the central city of Chongqing, a typical mountainous city, as an example. It provided a new approach by utilizing a multi-dimensional indicator system to analyze the CES supply-demand balance and coordination relationship of urban parks based on muti-source data. The result shows that: ① The supply and demand of cultural ecosystem services in urban parks in Chongqing has a significant spatial heterogeneity. The pattern of CES supply is distributed a high in the north and a low in the south, while the high demand is concentrated in the urban centers. Compared to the demand, the CES supply showed a more decentralized pattern. ② The results showed a significant spatial imbalance between the supply and demand of urban parks, with 52.38% of the clusters having an insufficient supply of cultural services, and 33.33% of the clusters in the condition of over-supply. The coupling coordinated degree between CES supply and demand demonstrated a gradual decline from the center to the periphery, with an average value of 0.50; ③ Based on the assessment of supply-demand balance and coupling coordination, our findings demonstrated that the uncoordinated development in peripheral urban clusters was mainly caused by the oversupply, while the central cluster maintained a moderate level of coordinated development with insufficient supply. Overall, most of the urban clusters in the central area of Chongqing have a certain degree of mismatch between the CES supply and demand of urban parks. Therefore, this study proposed targeted urban green space planning and management strategies based on the CES supply-demand assessment. The results can provide suggestions for rational allocation and management of urban parks for decision-making, supporting urban green space planning and management in mountainous cities.