The rational layout of green infrastructure (GI) is conducive to establishing a new model of green development of the territorial space. Under the background of ecological civilization and high-quality development, it is significant to explore the spatiotemporal dual-dimensional evolution pattern of GI in the long run. It could improve the quality of the ecological environment, enhance the spatial governance of territorial space, and achieve the goal of carbon neutrality. This study constructed a conceptual framework of GI that involved Cellular Automata-Markov (CA-Markov), Morphological Spatial Pattern Analysis (MSPA), and landscape pattern analysis methods to analyze the spatiotemporal dual-dimensional analysis of GI in the past, present, and future. We took the Beijing-Tianjin-Hebei urban agglomeration as the study area. We first analyzed the spatiotemporal dual-dimensional evolution characteristics of GI from 2000 to 2020. Then we simulated the future development in 2025 and 2030. Furthermore, we discussed the correspondence between the collaborative development process and the pattern evolution of GI, and summarized the optimization insights of GI. The results showed that:(1) from 2000 to 2020, the proportion of the GI area in the study area decreased from 90.82% to 86.60%, which showed a downward trend year by year. The spatial distribution GI was dense in the northwest and sparse in the southeast. The core area accounted for 57.04% to 65.93% of the whole GI, which also emerged as a decreasing trend year by year. The core was mainly distributed in the northern, western, and northwestern parts of the study area. (2) From 2020 to 2030, although the area of GI will decline slightly, the percentage of the core area will grow significantly (84.04% in 2030). Other types of GI, such as bridge, edge, and loop, will have a smaller proportion of area. Spatially, these types will be scattered among the core. (3) The acceleration of the collaborative development of urban agglomerations directly led to fluctuations in GI's area, particularly in the substantial development period (2015-2020) and the accelerated implementation period (2020-2025). (4) In the future, the improvement of the stability of the ecological network of GI in the Beijing-Tianjin-Hebei urban agglomeration should focus on the area percentage of GI in urban centers and the connectivity in the southeast of the study area. Our framework provides technical support for the rapid realization of inspection, assessment, and governance of GI. It also helps to establish a new green, low-carbon and sustainable development mode in the Beijing-Tianjin-Hebei urban agglomeration.