Strengthening and optimizing the spatial structure and functional connectivity of green space ecological networks can not only relieve the tight urban space and provide biodiversity protection but also promote the virtuous cycle of the urban ecosystem and provide a new method for the resilient development of the urban landscape. In this study, the central area of Chengdu was taken as the study area; Morphological Spatial Pattern Analysis (MSPA) with landscape metrics were combined to determine the optimal distance threshold and identify the ecological sources. Graph theory and circuit theory were applied to construct and optimize the green space ecological network with structural or functional connectivity, respectively. Based on the coupling effect, the optimization of the ecological network was put forward, and the network analysis method was used to evaluate the connectivity of three different types of ecological networks. The results were as follows: (1) The ecological network with structural connectivity was composed of 74 stepping stones, 43 protective sources, and 315 ecological corridors. The connectivity of green space structures gradually decreased from west to east and from periphery to center. (2) In the optimal ecological network with functional connectivity, 176 important ecological corridors were protected, and 40 pinch points and 48 protective sources were identified. The number of important corridors in the east and south was the largest, and the network structure was relatively complex. The barriers were divided into three different levels of ecological restoration areas. (3) The green ecological network with structural and functional connectivity has the best network connectivity. A green space ring network optimization pattern of one center, two belts, multi-points, multi-corridors, and multi-zones connected in a series was proposed. It was suggested to build a multi-level forest ecosystem in Longquan Mountain, develop eco-fruit agriculture and eco-tourism, enrich the biodiversity of the ecological source, and improve its anti-interference ability to the external environment. It is also important to increase ecological strategic points and stepping stones to strengthen the links between different ecological restoration areas, properly handle the use of cultivated land in different regions, strictly observe the red line of cultivated land, and maintain the integrity and diversity of ecological sources. Therefore, the optimization method of the green space ecological network in this study provides technical support for the effective determination of ecological protection areas, the accurate implementation of green space ecological networks, and a scientific planning strategy for decision-makers.