Addressing the imbalance between supply and demand for urban parks necessitates an assessment of their service accessibility and spatial equity. This study integrates multi-source geographic data, uses multiple data sources to generate a population distribution with high spatial resolution, and constructs park service areas with multiple time thresholds based on travel preference surveys. The network analysis method is used to evaluate the supply–demand ratio and spatial equity by using location entropy, Lorenz curves, and the Gini coefficient to identify the optimal location. The results reveal a significant difference in the supply–demand ratio of parks. Within the 5 min time threshold, only 14.68% of the pixels in the park supply area meet the needs of residents, while the proportions for the 15 min and 30 min time service area expands to 71.74% and 86.34%, respectively. The distribution of parks exhibits apparent spatial inequity. Equity is highest for the 15 min service area (Gini coefficient = 0.25), followed by the 30 min area (Gini coefficient = 0.27) and 5 min areas (Gini coefficient = 0.37). Among the 80 streets in the study area, the per capita green space location entropy of 11 streets is zero. A targeted site selection analysis for areas with park supply deficiencies led to the proposed addition of 11 new parks. After this optimization, the proportion of regions achieving supply–demand balance or better reached 80.38%, significantly alleviating the supply–demand conflict. This study reveals the characteristics of park supply–demand imbalance and spatial equity under different travel modes and time thresholds, providing a scientific basis for the precise planning and equity enhancement of parks in high-density cities.